On hereditary Baireness of the Vietoris topology

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: 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 of Saint Raymond, we show in ZFC that there exists a non-completely metrizable, metrizable space X with hereditarily Baire hyperspace (K(X),tv); thus settling a problem of Bouziad. Hereditary Baireness of (K(X),tv) for a Moore space X is also characterized in terms of an auxiliary product space and the strong Choquet game. Finally, using a result of Kunen, a non-consonant metrizable space having completely metrizable separable closed subspaces is constructed under CH. ? 2001 Elsevier Science B.V. All rights reserved.

Additional Information

Topology and its Applications, Vol 115, Issue 3, 247-258
Language: English
Date: 2001
Hyperspaces; Vietoris topology; Hereditarily Baire spaces; Strong Choquet game; Game morphism; Consonant spaces; Moore spaces

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