# Lajos Soukup

## Papers

94. S. Fuchino , S. Geschke , O. Guzman , L. Soukup , How to drive our families mad? , Arch. Mat. Log, submitted , Arxiv .

Given a family $$F$$ of pairwise almost disjoint sets on a countable set $$S$$, we study maximal almost disjoint (mad) families $$F^+$$ extending $$F$$.
We define $$a^+(F)$$ to be the minimal possible cardinality of $$F^+- F$$ for such $$F^+$$, and $$a^+(\kappa)=sup\{a^+(F):|F|\le\kappa\}$$. We show that all infinite cardinal less than or equal to the continuum continuum can be represented as $$a^+(F)$$ for some almost disjoint $$F$$ and that the inequalities $$\aleph_1=a<a^+(\aleph_1)=c$$ and $$a=a^+(\aleph_1)<c$$ are both consistent. Surprisingly, however, $$a^+(c)=c$$.
We also give a several constructions of mad families with some additional properties.

93. S. Fuchino , H. Sakai , L. Soukup , T. Usuba , More about the Fodor-type Reflection Principle , Fund. Math., submitted , Link .

We show that FRP is equivalent to the non-existence of almost essentially disjoint ladder system on any stationary subset of a regular uncountable cardinal consisting of ordinals of countable cofinality.
Using this characterization, we show that FRP is actually equivalent to many known “mathematical” reflection theorems over ZFC.
For example, it is shown that FRP is equivalent to the statement: “For any locally countably compact topological space X, if all subspaces of X of cardinality $$\le \aleph_1$$ are metrizable, then X itself is also metrizable” Another example of statements equivalent to FRP is: “For any graph G, if all subgraphs of G of cardinality $$\le \aleph_1$$ have countable coloring number then G itself also has countable coloring number”

92. P. L. Erdős, , C. Greenhill , T.R. Mezei , I. Miklos , D. Soltész , L. Soukup , The mixing time of the switch Markov chains: a unified approach , Eur.J.Comb, to appear .

Since 1997 a considerable effort has been spent to study the mixing time of \textbf{swap} (switch) Markov chains on the realizations of graphic degree sequences of simple graphs. Several results were proved on rapidly mixing Markov chains on unconstrained, bipartite, and directed sequences, using different mechanisms. The aim of this paper is to unify these approaches. We will illustrate the strength of the unified method by showing that on any P-stable family of unconstrained/bipartite/directed degree sequences the swap Markov chain is rapidly mixing. This is a common generalization of every known result that shows the rapid mixing nature of the swap Markov chain on a region of degree sequences. Two applications of this general result will be presented. One is an almost uniform sampler for power-law degree sequences with exponent $$\gamma>2$$. The other one shows that the swap Markov chain on the degree sequence of an Erdős-Rényi random graph G(n,p) is asymptotically almost surely rapidly mixing.

91. I. Juhász , L. Soukup , Z. Szentmiklóssy , Dominating and pinning down pairs for topological spaces , Top. Proc, 59 (2022) , pp 67--88 , Arxiv .

We call a pair of infinite cardinals $$(\kappa,\lambda)$$ with $$\kappa > \lambda$$ a dominating (resp. pinning down) pair
for a topological space $$X$$ if for every subset $$A$$ of $$X$$ (resp. family $$\mathcal{U}$$ of non-empty open sets in $$X$$) of cardinality
$$\le \kappa$$ there is $$B \subset X$$ of cardinality $$\le \lambda$$ such that $$A \subset \overline{B}$$ (resp. $$B \cap U \ne \emptyset$$
for each $$U \in \mathcal{U}$$). Clearly, a dominating pair is also a pinning down pair for $$X$$.
Our definitions generalize the concepts introduced in \cite{GTW} resp. \cite{BT} which focused on pairs of the form $$(2^\lambda,\lambda)$$.

The main aim of this paper is to answer a large number of the numerous problems from [GTW] and ]BT]
that asked if certain conditions on a space $$X$$ together with the assumption that $$(2^\lambda,\lambda)$$ or $$((2^\lambda)^+,\lambda)$$
is a pd-pair\ or\dom-oair for $$X$$ would imply $$d(X) \le \lambda$$.

[BT] A. Bella, V.V. Tkachuk, Exponential density vs exponential domination, preprint

[GTW] G. Gruenhage, V.V. Tkachuk, R.G. Wilson, Domination by
small sets versus density, Topology and its Applications 282 (2020)

90. I. Juhász , S. Shelah , L. Soukup , Z. Szentmiklóssy , Large strongly anti-Urysohn spaces exist , Top. Appl, to appear , Arxiv .

As defined in [1], a Hausdorff space is strongly anti-Urysohn (in short: SAU) if it has at least two non-isolated points and any two infinite} closed subsets of it intersect. Our main result answers the two main questions of [1] by providing a ZFC construction of a locally countable SAU space of cardinality $$2^c$$. The construction hinges on the existence of $$2^c$$ weak P-points in $$ω^∗$$, a very deep result of Ken Kunen.
It remains open if SAU spaces of cardinality $$>2^c$$ could exist, while it was shown in [1] that $$2^{(2^c)}$$ is an upper bound. Also, we do not know if crowded SAU spaces, i.e. ones without any isolated points, exist in ZFC but we obtained the following consistency results concerning such spaces.
(1) It is consistent that c is as large as you wish and there is a locally countable and crowded SAU space of cardinality $$c^+$$.
(2) It is consistent that both c and $$2^c$$ are as large as you wish and there is a crowded SAU space of cardinality $$2^c$$.
(3) For any uncountable cardinal κ the following statements are equivalent:
(i) $$κ=cof([κ]^ω,⊆)$$.
(ii) There is a locally countable and crowded SAU space of size κ in the generic extension obtained by adding κ Cohen reals.
(iii) There is a locally countable and countably compact T1-space of size κ in some CCC generic extension.

[1] I. Juhasz, L. Soukup, and Z. Szentmiklossy, Anti-Urysohn spaces, Top. Appl., 213 (2016), pp. 8--23.

89. J. C. Martinez , L. Soukup , A consistency result on long cardinal sequences , Ann. Pure Appl. Logic,, 172, 10 (2021) , Arxiv .

For any regular cardinal $$\kappa$$ and ordinal $$\eta<\kappa^{++}$$ it is consistent that $$2^{\kappa}$$ is as large as you wish, and every function $$f:\eta \to [\kappa,2^{\kappa}]\cap Card$$ with $$f(\alpha)=\kappa$$ for $$cf(\alpha)<\kappa$$ is the cardinal sequence of some locally compact scattered space.

88. I. Juhász , L. Soukup , Z. Szentmiklóssy , J. van Mill, , Connected and/or topological group pd-examples , Top. Appl, 283 (2020) , Arxiv .

The pinning down number $$pd(X)$$ of a topological space $$X$$ is the smallest cardinal $$\kappa$$ such that for every neighborhood assignment $$U$$ on $$X$$ there is a set of size $$\kappa$$ that meets every member of $$U$$. Clearly, $$pd(X)\le d(X)$$ and we call $$X$$ a pd-example if $$pd(X)<d(X)$$. We denote by $$S$$ the class of all singular cardinals that are not strong limit. It was proved in a paper of Juhász,Soukup and Szentmiklóssy (arXiv:1506.00206) that TFAE:
(1) $$S≠∅$$;
(2) there is a 0-dimensional $$T_2$$ pd-example;
(3) there is a $$T_2$$ pd-example.
The aim of this paper is to produce pd-examples with further interesting topological properties like connectivity or being a topological group by presenting several constructions that transform given pd-examples into ones with these additional properties.
We show that $$S\ne\emptyset$$ is also equivalent to the existence of a connected and locally connected $$T_3$$ pd-example, as well as to the existence of an abelian $$T_2$$ topological group pd-example.
However, $$S\ne \emptyset$$ in itself is not sufficient to imply the existence of a connected $$T_{3.5}$$ pd-example. But if there is $$\mu\in S$$ with $$\mu \ge c$$ then there is an abelian $$T2$$ topological group (hence $$T_{3.5}$$) pd-example which is also arcwise connected and locally arcwise connected. Finally, the same assumption $$S∖\ c\ne\emptyset$$ even implies that there is a locally convex topological vector space pd-example.

87. L. Soukup , A. Stanley , Left-separating order types , Top. Appl, 283 (2020) , Arxiv .

A well ordering $$\prec$$ of a topological space $$X$$ is left-separating if $$\{x'\in X: x'\prec x\}$$ is closed in $$X$$ for any $$x\in X$$. A space is {\em left-separated} if it has a left-separating well-ordering. The {\em left-separating type} $$ord_\ell(X)$$ of a left-separated space $$X$$ is the minimum of the order types of the left-separating well-orderings of $$X$$.
We prove that

if $${\kappa}$$ is a regular cardinal, then for each ordinal $${\alpha}<{\kappa}^+$$ there is a $$T_2$$ space $$X$$ with $$ord_\ell(X)={\kappa}\cdot {\alpha}$$;

if $${\kappa}={\lambda}^+$$ and $$cf({\lambda})={\lambda}>{\omega}$$, then for each ordinal $${\alpha}<{\kappa}^+$$ there is a 0-dimensional space $$X$$ with $$ord_\ell(X)={\kappa}\cdot {\alpha}$$;

if $${\kappa}=2^{\omega}$$ or $${\kappa}=\beth_{{\beta}+1}$$, where $$cf({\beta})={\omega}$$, then for each ordinal $${\alpha}<{\kappa}^+$$ there is a locally compact, locally countable, 0-dimensional space $$X$$ with $$ord_\ell(X)={\kappa}\cdot {\alpha}$$.

86. I. Juhász , L. Soukup , Z. Szentmiklóssy , Spaces of small cellularity have nowhere constant continuous images of small weight , Top. Appl, 281 (2020) , Arxiv .

We call a continuous map $$f:X\to Y$$ nowhere constant if it is not constant on any non-empty open subset of its domain $$X$$. Clearly, this is equivalent with the assumption that every fiber $$f^{−1}(y)$$ of $$f$$ is nowhere dense in $$X$$. We call the continuous map $$f:X\to Y$$ pseudo-open if for each nowhere dense $$Z\subset Y$$ its inverse image $$f^{−1}(Z)$$ is nowhere dense in $$X$$. Clearly, if $$Y$$ is crowded, i.e. has no isolated points, then
$$f$$ is nowhere constant.
The aim of this paper is to study the following, admittedly imprecise, question: How "small" nowhere constant, resp. pseudo-open continuous images can "large" spaces have? Our main results yield the following two precise answers to this question, explaining also our title. Both of them involve the cardinal function $$\hat c(X)$$, the "hat version" of cellularity, which is defined as the smallest cardinal $$\kappa$$ such that there is no $$\kappa$$-sized disjoint family of open sets in $$X$$. Thus, for instance, $$\hat c(X)=\omega_1$$ means that $$X$$ is CCC.
THEOREM A. Any crowded Tychonov space $$X$$ has a crowded Tychonov nowhere constant continuous image $$Y$$ of weight $$w(Y)\le \hat c(X)$$. Moreover, in this statement $$\le$$ may be replaced with $$<$$ iff there are no $$\hat c(X)$$-Suslin lines (or trees).
THEOREM B. Any crowded Tychonov space $$X$$ has a crowded Tychonov pseudo-open continuous image Y of weight $$w(Y)\le 2^{<\hat c(X)}$$. If Martin's axiom holds then there is a CCC crowded Tychonov space $$X$$ such that for any crowded Hausdorff pseudo-open continuous image $$Y$$ of X we have $$w(Y)\ge c(=2^{<\omega_1})$$.

85. I. Juhász , L. Soukup , Z. Szentmiklóssy , On cellular-compact spaces , Acta Math Hung, 162, 2 (2020) , pp 549--556 , Arxiv .

As it was introduced by Tkachuk and Wilson, a topological space $$X$$ is {\em cellular-compact} if for any cellular, i.e. disjoint, family $$\mathcal U$$ of non-empty open subsets of $$X$$ there is a compact subspace $$K\subset X$$ such that $$K\cap U\ne \emptyset$$ for each $$U\in \mathcal U$$.

Answering several questions raised by Tkachuk and Wilson we show that
(1) any first countable cellular-compact $$T_2$$ space is $$T_3$$, and so its cardinality is at most $$\mathfrak{c} = 2^{\omega}$$;
(2) $$cov(\mathcal M)>{\omega}_1$$ implies that every first countable and separable cellular-compact $$T_2$$ space is compact;
(3) if there is no $$S$$space then any cellular-compact $$T_3$$ space of countable spread is compact;
(4) $$MA_{{\omega}_1}$$ implies that every point of a compact $$T_2$$ space of countable spread has a disjoint local $$\pi$$-base.

84. I. Juhász , L. Soukup , Z. Szentmiklóssy , On the free set number of topological spaces and their $$G_\delta$$-modifications , Top. Appl, to appear , Arxiv .

For a topological space $$X$$ we propose to call a subset $$S \subset X$$ free in $$X$$ if it admits a well-ordering that turns it into a free sequence in $$X$$. The well-known cardinal function $${F}(X)$$ is then definable as
$$\sup\{|S| : S \text{ is free in } X\}$$ and will be called the free set number of $$X$$.

We prove several new inequalities involving $${F}(X)$$ and $${F}(X_\delta)$$, where $$X_\delta$$ is the $$G_{\delta}$$-modification of $$X$$:

$$\bullet$$ $${L}(X) \le 2^{2^{{F}(X)}}$$ if $$X$$ is $$T_2$$ and $${L}(X)\le 2^{{F}(X)}$$ if $$X$$ is $$T_3$$;

$$\bullet$$
$$|X|\le 2^{2^{{F}(X) \cdot {\psi_c}(X)}} \le 2^{2^{{F}(X) \cdot \chi(X)}}$$ for any $$T_2$$-space $$X$$;

$$\bullet$$
$${F}(X_{\delta})\le 2^{2^{2^{{F}(X)}}}$$ if $$X$$ is $$T_2$$ and $${F}(X_{\delta})\le 2^{2^{{F}(X)}}$$ if $$X$$ is $$T_3$$.

83. A. Dow , I. Juhász , L. Soukup , Z. Szentmiklóssy , W. Weiss , On the tightness of $$G_\delta$$-modifications , Acta Math. Hung., 158, 2 (2019) , pp 294--301 , Arxiv .

The $$G_δ$$-modification $$X_δ$$ of a topological space $$X$$ is the space on the same underlying set generated by, i.e. having as a basis, the collection of all$$G_δ$$ subsets of $$X$$. Bella and Spadaro recently investigated the connection between the values of various cardinal functions taken on $$X$$ and $$X_δ$$, respectively. In their paper, as Question 2, they raised the following problem: Is $$t(X_δ)≤2^{t(X)}$$ true for every (compact) $$T_2$$ space $$X$$? Note that this is actually two questions.
In this note we answer both questions: In the compact case affirmatively and in the non-compact case negatively. In fact, in the latter case we even show that it is consistent with ZFC that no upper bound exists for the tightness of the$$G_δ$$-modifications of countably tight, even Frechet spaces.

82. I. Juhász , L. Soukup , Z. Szentmiklóssy , On the resolvability of Lindelöf-generated and (countable extent)-generated spaces , Top. Appl, 259, 1 (2019) , pp 267--274 , Arxiv .
81. J. C. Martinez , L. Soukup , On cardinal sequences of length $$<\omega_3$$ , Top. Appl, to appear , Arxiv .

We prove the following consistency result for cardinal sequences of length $$< \omega_3$$: if GCH holds and $$\lambda \geq \omega_2$$ is a regular cardinal, then in some cardinal-preserving generic extension $$2^{\omega} = \lambda$$ and for every ordinal $$\eta< \omega_3$$ and every sequence $$f = \langle \kappa_{\alpha} : \alpha < \eta\rangle$$ of infinite cardinals with $$\kappa_{\alpha}\leq \lambda$$ for $$\alpha < \eta$$ and $$\kappa_{\alpha} = \omega$$ if $$\mbox{cf}(\alpha) = \omega_2$$, we have that f is the cardinal sequence of some LCS space.

Also, we prove that for every specific uncountable cardinal $$\lambda$$ it is relatively consistent with ZFC that for every $$\alpha,\beta < \omega_3$$ with $${cf}(\alpha) < \omega_2$$ there is an LCS space Z such that $${CS}(Z) = \langle \omega\rangle_\alpha{}^\frown \langle \lambda\rangle_\beta$$.

80. P. L. Erdős, , C. Greenhill , T.R. Mezei , I. Miklos , D. Soltész , L. Soukup , Mixing time of the swap Markov chain and P-stability , Acta Math. Univ. Comenian, 88, 3 (2019) , pp 659--665 .

The aim of this paper is to confirm that P-stability of a family of unconstrained/bipartite/directed degree sequences is sufficient for the swap Markov chain to be rapidly mixing on members of the family. This is a common generalization of every known result that shows the rapid mixing nature of the swap Markov chain on a region of degree sequences. In addition, for example, it encompasses power-law degree sequences with exponent γ>2, and, asymptotically almost surely, the degree sequence of any Erdős-Rényi random graph G(n,p) where p is bounded away from 0 and 1 by at least 5 log n /n−1.
They also show that there exists a family of degree sequences which is not P-stable and its members have exponentially many realizations, yet the swap Markov chain is still rapidly mixing on them.

79. I. Juhász , L. Soukup , Z. Szentmiklóssy , Coloring Cantor sets and resolvability of pseudocompact spaces , CMUC, 59, 4 (2018) , pp 523--529 , Arxiv .

Let us denote by $$Φ(λ,μ)$$ the statement that $$\mathbb{B}(λ) = D(λ)^ω$$, i.e. the Baire space of weight $$λ$$, has a coloring with $$μ$$ colors such that every homeomorphic copy of the Cantor set $$\mathbb{C}$$ in $$\mathbb{B}(λ)$$ picks up all the $$μ$$ colors.
We call a space $$X\,$$ {\em $$π$$-regular} if it is Hausdorff and for every non-empty open set $$U$$ in $$X$$ there is a non-empty open set $$V$$ such that $$\overline{V} \subset U$$. We recall that a space $$X$$ is called {\em feebly compact} if every locally finite collection of open sets in $$X$$ is finite. A Tychonov space is pseudocompact iff it is feebly compact.
The main result of this paper is the following.

Theorem. Let $$X$$ be a crowded feebly compact $$π$$-regular space and $$μ$$ be a fixed (finite or infinite) cardinal. If $$Φ(λ,μ)$$ holds for all $$λ< \widehat{c}(X)$$ then $$X$$ is $$μ$$-resolvable, i.e. contains $$μ$$ pairwise disjoint dense subsets. (Here $$\widehat{c}(X)$$ is the smallest cardinal $$κ$$ such that $$X$$ does not contain $$κ$$ many pairwise disjoint open sets.)

This significantly improves earlier results of van Mill , resp. Ortiz-Castillo and Tomita.

78. D. Soukup , L. Soukup , Infinite combinatorics plain and simple , J. Symb. Logic, 83, 3 (2018) , pp 1247--1281 , Arxiv .

We explore a general method based on trees of elementary submodels in order to present highly simplified proofs to numerous results in infinite combinatorics. While countable elementary submodels have been employed in such settings already, we significantly broaden this framework by developing the corresponding technique for countably closed models of size continuum. The applications range from various theorems on paradoxical decompositions of the plane, to coloring sparse set systems, results on graph chromatic number and constructions from point-set topology. Our main purpose is to demonstrate the ease and wide applicability of this method in a form accessible to anyone with a basic background in set theory and logic.

77. I. Juhász , L. Soukup , Z. Szentmiklóssy , First countable almost discretely Lindelöf $$T_3$$ spaces have cardinality at most continuum , Top. Appl, 241 (2018) , pp 145--149 , Arxiv .
76. M. Elekes , D. Soukup , L. Soukup , Z. Szentmiklóssy , Decompositions of edge-colored infinite complete graphs into monochromatic paths , Disc. Math, 340, 8 (2017) , pp 2053--2069 , Arxiv .
75. L. Soukup , A. Stanley , Resolvability in c.c.c. generic extensions , CMUC, 58, 4 (2017) , pp 519--529 , Arxiv .
74. I. Juhász , L. Soukup , Z. Szentmiklóssy , Pinning Down versus Density , Israel J. Math, 215, 2 (2016) , pp 583--605 , Arxiv .
73. I. Juhász , L. Soukup , Z. Szentmiklóssy , Anti-Urysohn spaces , Top. Appl, 213 (2016) , pp 8--23 , Arxiv .
72. I. Juhász , L. Soukup , Z. Szentmiklóssy , Between countably compact and ω-bounded , Top. Appl, 195 (2015) , pp 196--208 , Arxiv .
71. P. L. Erdős, , S. Kiss , I. Miklos , L. Soukup , Approximate Counting of Graphical Realizations , PLOS ONE, 10, 7 (2015) , Link .
70. D. Soukup , L. Soukup , Partitioning bases of topological spaces , CMUC, 55, 4 (2014) , pp 537--566 , Arxiv .
69. I. Juhász , L. Soukup , Z. Szentmiklóssy , Regular spaces of small extent are ω-resolvable , Fund. Math., 228 (2014) , pp 27--46 , Arxiv .
68. P. L. Erdős, , I. Miklos , L. Soukup , Towards random uniform sampling of bipartite graphs with given degree sequence , Electr. J. Com, 20, 1 (2013) , Arxiv .
67. L. Soukup , Essentially disjoint families, conflict free colorings and Shelah's Revised GCH , Acta Math Hung, 140, 3 (2013) , pp 293--303 , Arxiv .
66. D. Soukup , L. Soukup , S. Spadaro , Comparing weak versions of separability , Top. Appl, 160 (2013) , pp 2538--2566 , Arxiv .
65. L. Soukup , Elementary submodels in infinite combinatorics , Disc. Math, 311, 15 (2012) , pp 1585--1598 , Arxiv .
64. M. Elekes , T. Mátrai , L. Soukup , On splitting infinite-fold covers , Fund. Math., 212, 2 (2011) , pp 95--127 , Arxiv .
63. P. L. Erdős, , L. Soukup , J. Stoyle , Balanced Vertices in Trees and a Simpler Algorithm to Compute the Genomic Distance , Appl. Math. Letters, 0 (2011) , pp 82--82 .
62. A. Hajnal , I. Juhász , L. Soukup , Z. Szentmiklóssy , Conflict free colorings of (strongly) almost disjoint set-systems , Acta Math Hung, 131, 3 (2011) , pp 230--274 , Arxiv .
61. J. C. Martinez , L. Soukup , Superatomic Boolean algebras constructed from strongly unbounded functions , Math. Log. Quarterly, 57, 5 (2011) , pp 456--469 , Link .
60. L. Soukup , Pcf theory and cardinal invariants of the reals , CMUC, 52, 1 (2011) , pp 153--162 , Arxiv .
59. L. Soukup , Wide scattered spaces and morasses , Top. Appl, 158, 5 (2011) , pp 697--707 , Arxiv .
58. P. L. Erdős, , L. Soukup , No Finite+Infinite Antichain Duality in the Homomorphism Poset of Directed Graphs , Order, None (2010) , pp 1--9 .
57. S. Fuchino , I. Juhász , L. Soukup , Z. Szentmiklóssy , T. Usuba , Fodor-type Reflection Principle, metrizability and meta-Lindelöfness , Top. Appl, 157, 8 (2010) , pp 1415--1429 .
56. J. C. Martinez , L. Soukup , Cardinal sequences of LCS spaces under GCH , Ann. Pure Appl. Logic,, 161 (2010) , pp 1180--1193 .
55. J. C. Martinez , L. Soukup , Universal locally compact scattered spaces , Top. Proc, 35 (2010) , pp 19--36 .
54. L. Soukup , L. Soukup, Cardinal Sequences and Combinatorial Principles , , Dsc. Thesis,2010 .
53. P. L. Erdős, , L. Soukup , Quasi-kernels and quasi-sinks in infinite graphs , Disc. Math, 309, 10 (2009) , pp 3040--3048 .
52. B Farkas , L. Soukup , More on cardinal invariants of analytic P-ideals , CMUC, 50, 2 (2009) , pp 281--295 .
51. I. Juhász , Poitr Koszmider , L. Soukup , A first countable, initially $$\omega_1$$-compact but non-compact space , , Top. Appl, 156, 10 (2009) , pp 1863--1879 .
50. I. Juhász , S. Shelah , L. Soukup , Resolvability vs. almost resolvability , Top. Appl, 156, 11 (2009) , pp 1966--1969 .
49. J. C. Martinez , L. Soukup , The D-property in unions of scattered spaces , Top. Appl, 156, 18 (2009) , pp 3086--3090 .
48. L. Soukup , Indestructible colourings and rainbow Ramsey theorems , Fund. Math., 202, 2 (2009) , pp 161--180 .
47. I. Juhász , L. Soukup , Z. Szentmiklóssy , Resolvability and monotone normality , Israel J. Math, 166 (2008) , pp 1--16 .
46. L. Soukup , Infinite combinatorics: from finite to infinite , in: Horizons of combinatorics, pp 189--213, Bolyai Soc. Math. Stud., 17, Springer, Berlin, 2008 .
45. L. Soukup , Nagata's conjecture and countably compact hulls in generic extensions , Top. Appl, 155, 4 (2008) , pp 347--353 .
44. D. Duffus , P. L. Erdős, , J. Nešetřil , L. Soukup , Antichains in the homomorphism order of graphs , CMUC, 48, 4 (2007) , pp 571--583 .
43. L. Soukup , Partitioning $$\kappa$$-fold covers into $$\kappa$$ many subcovers , Real Anal. Exchange, 31 (2007) , pp 121--125 .
42. P. L. Erdős, , L. Soukup , How to split antichains in infinite posets , Combinatorica , Combinatorica, 27, 2 (2007) , pp 147--161 .
41. I. Juhász , L. Soukup , Z. Szentmiklóssy , First countable spaces without point-countable π-bases , Fund. Math., 196, 2 (2007) , pp 139--149 .
40. I. Juhász , L. Soukup , Z. Szentmiklóssy , Resolvability of spaces having small spread or extent , Top. Appl, 154, 1 (2007) , pp 144--154 .
39. L. Soukup , Cardinal sequences and universal spaces , in: Open Problems in Topology II, pp 737--737, ed: Elliott Pearl, Elsevier, 2007 .
38. I. Juhász , L. Soukup , Z. Szentmiklóssy , D-forced spaces: a new approach to resolvability , Top. Appl, 153, 11 (2006) , pp 1800--1824 .
37. I. Juhász , L. Soukup , W. Weiss , Cardinal sequences of length $$\omega_2$$ under GCH , , Fund. Math., 189, 1 (2006) , pp 35--52 .
36. L. Soukup , A lifting theorem on forcing LCS spaces , in: More sets, graphs and numbers, pp 341--358, Bolyai Soc. Math. Stud., 15, Springer, Berlin, 2006 .
35. J. Gerlits , I. Juhász , L. Soukup , Z. Szentmiklóssy , Characterizing continuity by preserving compactness and connectedness , Top. Appl, 138, 1 (2004) , pp 21--44 .
34. I. Juhász , S. Shelah , L. Soukup , Z. Szentmiklóssy , Cardinal sequences and Cohen real extensions , Fund. Math., 181, 1 (2004) , pp 75--88 .
33. L. Soukup , A piecewise Toronto space , , Studia Sci. Math. Hungar, 41, 3 (2004) , pp 325--337 .
32. I. Juhász , S. Shelah , L. Soukup , Z. Szentmiklóssy , A tall space with a small bottom , Proc Amer Math Soc, 131, 6 (2003) , pp 1907--1916 .
31. I. Juhász , L. Soukup , Z. Szentmiklóssy , A consistent example of a hereditarily $$\mathfrak c$$-Lindelöf first countable space of size $$>\mathfrak c$$ , in: Set theory (Piscataway, NJ, 1999), pp 95--98, DIMACS Ser. Discrete Math. Theoret. Comput. Sci., 58, Amer. Math. Soc., Providence, RI, 2002 .
30. S. Fuchino , S. Geschke , L. Soukup , On the weak Freese-Nation property of complete Boolean algebras , Ann. Pure Appl. Logic,, 110, 1 (2001) , pp 89--105 .
29. S. Fuchino , S. Geschke , L. Soukup , On the weak Freese-Nation property of $$\mathcal P(\omega)$$ , Arch. Mat. Log, 40, 6 (2001) , pp 425--435 .
28. L. Soukup , Indestructible properties of S- and L-spaces , Top. Appl, 112, 3 (2001) , pp 245--257 .
27. L. Soukup , Smooth graphs , CMUC, 40, 1 (1999) , pp 187--199 .
26. I. Juhász , L. Soukup , Z. Szentmiklóssy , What is left of CH after you add Cohen reals? , Top. Appl, 85, 1 (1998) , pp 165--174 .
25. I. Juhász , L. Soukup , Z. Szentmiklóssy , Combinatorial principles from adding Cohen reals , in: Logic Colloquium '95, pp 79--103, Lecture Notes Logic, 11, Springer, Berlin, 1998 .
24. J. Roitman , L. Soukup , Luzin and anti-Luzin almost disjoint families , Fund. Math., 158, 1 (1998) , pp 51--67 .
23. S. Fuchino , S. Shelah , L. Soukup , Sticks and clubs , Ann. Pure Appl. Logic,, 90, 1 (1997) , pp 57--77 .
22. S. Fuchino , L. Soukup , More set-theory around the weak Freese-Nation property , Fund. Math., 154, 2 (1997) , pp 159--176 .
21. A. Dow , I. Juhász , L. Soukup , Z. Szentmiklóssy , More on sequentially compact implying pseudoradial , Top. Appl, 73, 2 (1996) , pp 191--195 .
20. I. Juhász , Zs. Nagy , L. Soukup , Z. Szentmiklóssy , Intersection properties of open sets. II , in: Papers on general topology and applications (Amsterdam, 1994), pp 147--159, Ann. New York Acad. Sci., 788,, New York Acad. Sci., New York, 1996 .
19. I. Juhász , L. Soukup , How to force a countably tight, initially $$\omega_1$$-compact and noncompact space? , Top. Appl, 69, 3 (1996) , pp 227--250 .
18. I. Juhász , L. Soukup , Z. Szentmiklóssy , Forcing countable networks for spaces satisfying $$R(X^\omega)=\omega$$ , CMUC, 37 (1996) , pp 159--170 .
17. P. Nyikos , L. Soukup , B. Veličković , Hereditary normality of $$\gamma \mathbb N$$-spaces , Top. Appl, 65, 1 (1995) , pp 9--19 .
16. S. Shelah , L. Soukup , Some remarks on a problem of J. D. Monk , Period. Math. Hungar, 30, 2 (1995) , pp 155--163 .
15. S. Fuchino , L. Soukup , On a theorem of Shapiro , Math Japonica, 40, 2 (1994) , pp 199--206 .
14. I. Juhász , L. Soukup , Z. Szentmiklóssy , What makes a space have large weight? , , Top. Appl, 57 (1994) , pp 271--285 .
13. S. Shelah , L. Soukup , On the number of nonisomorphic subgraphs , Israel J. Math, 86 (1994) , pp 349--371 .
12. L. Soukup , Martin Axiómával konzisztens tulajdonságokról , Ph. D. dissertation (kandidátusi értekezés),1993 .
11. S. Shelah , L. Soukup , The existence of large $$\omega_1$$-homogeneous but not $$\omega$$-homogeneous permutation groups is consistent with ZFC+GCH , J. London Math. Soc., 48, 2 (1993) , pp 193--203 .
10. I. Juhász , Zs. Nagy , L. Soukup , Z. Szentmiklóssy , The long club , in: Sets, graphs and numbers (Budapest, 1991), pp 411--419, Colloq. Math. Soc. János Bolyai, 60, North-Holland, Amsterdam, 1992 .
9. L. Soukup , Certain L-spaces under CH , Top. Appl, 47, 1 (1992) , pp 1--7 .
8. L. Soukup , On $$\omega^2$$-saturated families , CMUC, 32, 2 (1991) , pp 355--359 .
7. A. Hajnal , Zs. Nagy , L. Soukup , On the number of certain subgraphs of graphs without large cliques and independent subsets , in: A tribute to Paul Erdős, pp 223--248, Cambridge Univ. Press, Cambridge, 1990 .
6. L. Soukup , On $$\mathfrak c^+$$-chromatic graphs with small bounded subgraphs , Period. Math. Hungar, 21, 1 (1990) , pp 1--7 .
5. L. Soukup , A nonspecial $$\omega_2$$-tree with special $$\omega_1$$-subtrees , , CMUC, 31, 3 (1990) , pp 607--612 .
4. A. Hajnal , P. Komjáth , L. Soukup , I. Szalkai , Decompositions of edge colored infinite complete graphs , in: Combinatorics (Eger, 1987), pp 277--280, Colloq. Math. Soc. János Bolyai, 52, North-Holland, Amsterdam, 1988 .
3. S. Shelah , L. Soukup , More on countably compact, locally countable spaces , Israel J. Math, 62, 3 (1988) , pp 302--310 .
2. L. Soukup , On chromatic number of product of graphs , CMUC, 29, 1 (1988) , pp 1--12 .
1. A. Hajnal , I. Juhász , L. Soukup , On saturated almost disjoint families , CMUC, 28, 4 (1987) , pp 629--633 .

### Notes

5. L. Soukup , A note on Noetherian type of spaces , 2015 , Arxiv .
4. D. Soukup , L. Soukup , Club guessing for dummies , 2010 , Arxiv .
3. L. Soukup , Dense families of countable sets below $$\mathfrak c$$ , 2010 , Arxiv .
2. L. Soukup , Boolean algebras with prescribed topological densities , 1999 , Arxiv .
1. M. Dzamonja , L. Soukup , Some note on Banach spaces .