# Dr Laszlo Zsilinszky

- Professor
- Mathematics and Computer Science , UNCP
- laszlo@uncp.edu
- 910-521-6768
- 1 University Dr.
- Pembroke NC 28372
- http://www2.uncp.edu/home/laszlo/webpage.htm

There are 32 included publications by Dr Laszlo Zsilinszky :

Title | Date | Views | Brief 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 £ |

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... |