Dr Laszlo Zsilinszky

There are 32 included publications by Dr Laszlo Zsilinszky :

TitleDateViewsBrief Description
Baire Spaces and Hyperspace Topologies 1996 112 Sufficient conditions for abstract (proximal) hit-and-miss hyperspace topologies and the Wisjman hyperspace topology, respectively are given to be Baire spaces, thus extending results of [MC],[B1],[C]. Further the quasi-regularity of (proximal)hit-an...
Baire Spaces and Weak Topologies Generated by Gap and Excess Functionals 1999 78 Let (K, d) be a separable Baire metric space or a completely metrizable space. It is shown that the family CL(X) of all nonempty closed subsets of X endowed with the finite Hausdorff topology is a Baire space. Baireness of other weak topologies on CL...
Cech-Completeness and Related Properties Of The Generalized Compact-open Topology 2010 141 The generalized compact-open topology tC on partial continuous functions with closed domains in X and values in Y is studied. If Y is a noncountably compact ?Cech-complete space with a Gd-diagonal, then tC is ?Cechcomplete, sieve complete and satis?e...
Completeness Properties of the Generalized Compact-Open Topology of Partial Functions with Closed Domains 2001 131 The primary goal of the paper is to investigate the Baire property and weak a-favorability for the generalized compact-open topology tC on the space P of continuous partial functions f :A ? Y with a closed domain A ? X. Various sufficient and necessa...
Corrigendum to “On Bairness of the Wijsman Hyperspace” 2009 61 Baireness of the Wijsman hyperspace topology is characterized for a metrizable base space with a countable-in-itself p-base; further, a separable 1st category metric spaceis constructed with a Baire Wijsman hyperspace
Developability and related properties of the generalized compact-open topology 2009 71 Developability and related properties (like weak developability,Gd-diagonal, G*d-diagonal, submetrizability) of the generalized compact-open topology tC on partial continuous functions P with closed domains in X and values in Y are studied. First cou...
Developmental Hyperspaces are Metrizable 2003 61 Developability of hyperspace topologies (locally finite, (bounded) Vietoris, Fell, respectively) on the nonempty closed sets is characterized. Submetrizability and having a Gd-diagonal in the hyperspace setting is also discussed.
More on products of Baire spaces 2017 26 New results on the Baire product problem are presented. It is shown that an arbitrary product of almost locally ccc Baire spaces is Baire; moreover, the product of a Baire space and a 1st countable space which is ß-unfavorable in thestrong Choquet ga...
Note on Hit-And-Miss Topologies 2000 125 This is a continuation of [19]. We characterize first and second countability of the general hit-and-miss hyperspace topologyt+? for weakly-R0 base spaces. Further, metrizability oft+? is characterized with no preliminary conditions on the base space...
On Bairness of the Wijsman Hyperspace 2007 63 Baireness of the Wijsman hyperspace topology is characterized for a metrizable base space with a countable-in-itself p-base; further, a separable 1st category metric spaceis constructed with a Baire Wijsman hyperspace
On the class of functions having infinite limit on a given set 1994 22 According to [1] for a linear set A there exists a function f : R ? R such that A = Lf (R) if and only if A is a countable Gd-set. Our purpose is to prove a similar result in a more general setting and to investigate the cardinality and topological p...
On complete metrizability of the Hausdorff metric topology 2015 26 There exists a completely metrizable bounded metrizablespaceXwith compatible metricsd, d'so that the hyperspaceCL(X) ofnonempty closed subsets ofXendowed with the Hausdorff metricHd,Hd', resp. isa-favorable,ß-favorable, resp. in the strong Choquet ga...
On Complete Metrizability of Hyperspaces 2014 298 The purpose of the talk is to present new completeness results about the topology of bornological convergence S on the hyperspace C (X) of all nonempty closed subsets of a metric space (X; d). Two of the oldest and best applied hypertopologies, the ...
On Density of Ratio Sets of Powers of Primes 1995 76 Denote by R+ and N the set of all positive real numbers and the natural numbers,respectively. Let P = {p1, . . . , pn, . . . } be the set of all primes enumerated inincreasing order. Denote by R(A, B) = {a b; a ? A, b ? B} the ratio set of A, B ? R+ ...
On generalized metric properties of the Fell hyperspace 2014 42 It is shown that if XX contains a closed uncountable discrete subspace, then the Tychonoff plank embeds in the hyperspace CL(X) of the non-empty closed subsets of X with the Fell topology tF as a closed subspace. As a consequence, a plethora of prope...
On hereditary Baireness of the Vietoris topology 2001 115 It is shown that a metrizable space X, with completely metrizable separable closed subspaces, has a hereditarily Baire hyperspace K(X) of nonempty compact subsets of X endowed with the Vietoris topology tv. In particular, making use of a construction...
On measure spaces where Egoroff's Theorem holds 1994 68 A measure space (X, S, µ) is called almost f inite if X is a union of a setof finite measure and finite many atoms of infinite measure. It is shown that Egoroff’sTheorem for sequences of measurable functions holds if and only if the underlyingmeasure...
On Normability of a Space of Measurable Real Functions 1995 70 Let (X,S,µ) be a s-?nite measure space. Denote by M the class of all S-measurable functions that are ?nite almost everywhere on X. Gribanov in [G] considers the topology of convergence in measure on sets of ?nite measure on M. This topological space ...
On Products of Baire Spaces 2015 444 It is well-known, that if X ×Y is a Baire space, then X, Y are Baire as well, and the converse is not true in general. However, given a Baire topological space X, there is a rich literature of completeness properties for Y making X ×Y Baire. We will ...
On ß-favorability of the strong Choquet game 2011 0 In the main result, partially answering a question of Telg´arsky,the following is proven: if X is a 1st countable R0-space, then player ß (i.e. the EMPTY player) has a winning strategy in the strong Choquet game on X if and only if X contains a nonem...
On (Strong) a-Favorability of the Vietoris Hyperspace 2013 62 For a normal space X, a (i.e. the nonempty player) having a winning strategy (resp. winning tactic) in the strong Choquet game Ch(X) played on X is equivalent to a having a winning strategy (resp. winning tactic) inthe strong Choquet game played on t...
On (Strong) a-Favorability of the Wijsman Hyperspace 2010 73 The Banach–Mazur game as well as the strong Choquet game are investigated on theWijsman hyperspace from the nonempty player’s (i.e. a’s) perspective. For the strongChoquet game we show that if X is a locally separable metrizable space, then a has a(s...
On Subspaces of Measurable Real Functions 1995 52 Let (X, S, µ) be a measure space. Let F : IR ? IR be a continuous function. Topological properties of the space of all measurable real functions f such that F ? f is Lebesgue-integrable are investigated in the space of measurable real functions endow...
On Telgársky’s Question concerning ß-favorability of the Strong Choquet Game 2013 228 Answering a question of Telgársky in the negative, it is shown that there is a space which is ß-favorable in the strong Choquet game, but all of its nonempty Wd-subspaces are of the second category in themselves.
On a typical property of functions 1995 62 Let s be the space of all real sequences endowed with the Frechet metric g. Consider the space T of all functions / : R —* R with the uniform topology Denote by U the class of all functions/ £ T for which the set\ {a>i}i £ is ...
Polishness of the Wijsman Topology Revisited 1998 77 Let X be a completely metrizable space. Then the space of nonempty closed subsets of X endowed with the Wijsman topology is a-favorable in the strong Choquet game. As a consequence, a short proof ofthe Beer-Costantini Theorem on Polishness of the Wij...
Products of Baire Spaces Revisited 2004 104 Generalizing a theorem of Oxtoby, it is shown that an arbitrary product of Baire spaces which are almost locally universally Kuratowski–Ulam (in particular, have countable-in-itself p-bases) is a Baire space. Also, partially answering a question of F...
Strong a-favorability of the (generalized) compact-open topology 2003 50 Strong a-favorability of the compact-open topology on the space of continuous functions, as well as of the generalized compact-open topology on continuous partial functions with closed domains is studied.
Superporosity in a class of non-normable spaces 1996 73 The concept of porous set was introduced by Dol?zenko in [D]. Since then ithas been thoroughly investigated and diversely generalized (see [Za1] or [Re] for asurvey). It is possible to define several notions concerning porosity also in metricspaces (...
Topological Games and Hyperspace Topologies 1998 86 The paper proposes a uni?ed description of hypertopologies, i.e. topologies on the nonempty closed subsets of a topological space, based on the notion of approach spaces introduced by R. Lowen. As a special case of this description we obtain the abst...
Turtle Beats Carl Lewis! (Infinities - stuff that makes people go nuts) 2000 67 I hope that the above wise men convinced everybody that the following presentationis going to be about very serious mathematics. What I try to achieve in thispaper is to introduce a new world, where nearly everything defies our experience,a world in ...
Vietoris topology on partial maps with compact domains 2010 109 The space PK of partial maps with compact domains (identified with their graphs) forms a subspace of the hyperspace of nonempty compact subsets of a product space endowed with the Vietoris topology. Various completeness properties of PK, including Ce...