On (Strong) a-Favorability of the Wijsman Hyperspace

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

Abstract: 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(stationary) winning strategy on X iff it has a (stationary) winning strategy on the Wijsmanhyperspace for each compatible metric on X. The analogous result for the Banach–Mazurgame does not hold, not even if X is separable, as we show that a may have a (stationary)winning strategy on the Wijsman hyperspace for each compatible metric on X, and nothave one on X. We also show that there exists a separable 1st category metric spacesuch that a has a (stationary) winning strategy on its Wijsman hyperspace. This answers aquestion of Cao and Junnila (2010) [6].

Additional Information

Topology and its Applications Vol. 157
Language: English
Date: 2010
Wijsman topology, ball topology, Baire space, Banach-Mazur game, strong Choquet game, (strongly) a-favorable space, Bernstein set, Baire metric.

Email this document to