| We prove that if the Vietoris hyperspace ${mathcal F}(X)$ of all non-empty closed subsets of a space $X$ is Baire, then all finite powers of $X$ must be Baire spaces. In particular, there exists a metrizable Baire space $X$ whose Vietoris hyperspace $mathcal{F}(X)$ is not Baire. This settles a problem of McCoy stated in [9]. |
Keywords
Baire space, Product space, Hyperspace, Vietoris topology
Math Review Classification
Primary 54E52
; Secondary 26A21, 46A30, 54B10, 54B20.
Last Updated
20/8/04
Length
7 pages
Availability
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