| Baire Spaces and Hyperspace Topologies |
1996 |
1201 |
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 |
482 |
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 |
2126 |
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 |
1557 |
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 |
279 |
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 |
376 |
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 |
312 |
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 |
1285 |
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 |
1658 |
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 |
376 |
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 |
1087 |
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 |
1178 |
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 |
603 |
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 |
618 |
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 |
1194 |
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 |
1353 |
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 |
3117 |
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 |
280 |
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 |
1008 |
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 |
227 |
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 |
1081 |
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 |
1286 |
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 |
227 |
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 |
652 |
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 |
304 |
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 |
1180 |
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 |
1343 |
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 |
147 |
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 |
1293 |
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 |
535 |
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 |
284 |
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 |
1175 |
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... |