Papers
90. |
P. L. Erdős, ,
C. Greenhill ,
T.R. Mezei ,
I. Miklos ,
D. Soltész ,
L. Soukup ,
The mixing time of the swap (switch) Markov chains: a unified approach
, Arxiv, submitted
.
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. |
89. |
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 \(F\). |
88. |
L. Soukup ,
A. Stanley ,
Left separating orders of topological spaces
, Top. Appl, submitted
, 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 \(X\). 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 \(ord_\ell(X)={\kappa}\cdot {\alpha}\). |
87. |
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. |
86. |
J. C. Martinez ,
L. Soukup ,
A consistency result on long cardinal sequences
, Ann. Pure Appl. Logic,, submitted
, 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. |
85. |
I. Juhász ,
L. Soukup ,
Z. Szentmiklóssy ,
J. van Mill, ,
Connected and/or topological group pd-examples
, Top. Appl, to appear
, 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: |
84. |
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 \({CS}(Z) = \langle \omega\rangle_\alpha{}^\frown \langle \lambda\rangle_\beta\). |
83. |
I. Juhász ,
L. Soukup ,
Z. Szentmiklóssy ,
Spaces of small cellularity have nowhere constant continuous images of small weight
, Top. Appl, to appear
, 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 |
82. |
I. Juhász ,
L. Soukup ,
Z. Szentmiklóssy ,
On cellular-compact spaces
, Acta Math Hung, to appear
, 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 |
81. |
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. |
80. | 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 . |
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. 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 . |