On (Strong) a-Favorability of the Vietoris Hyperspace

UNCP Author/Contributor (non-UNCP co-authors, if there are any, appear on document)
Dr. Laszlo Zsilinszky, Professor (Creator)
Institution
The University of North Carolina at Pembroke (UNCP )
Web Site: http://www.uncp.edu/academics/library

Abstract: 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 the hyperspace CL(X) of nonempty closed subsets endowed with the Vietoris topology tV . It is shown that for a non-normal X where a has a winning strategy (resp. winning tactic) in Ch(X), a may or may not have a winning strategy (resp. winning tactic) in the strong Choquetgame played on the Vietoris hyperspace. If X is quasi-regular, then having a winning strategy (resp. winning tactic) for a in the Banach-Mazur game BM(X) played on X is sufficient for a having a winning strategy (resp. winning tactic) in BM(CL(X), tV ), but not necessary, not even for a separable metric X. Inthe absence of quasi-regularity of a space X where a has a winning strategy in BM(X), a may or may not have a winning strategy in the Banach-Mazur game played on the Vietoris hyperspace.

Additional Information

Publication
Mathematica Slovaca Vol. 63, Issue 2
Language: English
Date: 2013
Keywords
Vietoris topology, Banach-Mazur game, strong Choquet game, (strongly) (weakly) a-favorable space, Baire space, Tychonoff plank, Bernstein set.

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