Baire spaces and Vietoris hyperspaces

Cao, Jiling; García-Ferreira, Salvador; Gutev, Valentin

doi:10.1090/S0002-9939-06-08743-0

Baire spaces and Vietoris hyperspaces
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by Jiling Cao, Salvador García-Ferreira and Valentin Gutev PDF

Proc. Amer. Math. Soc. 135 (2007), 299-303 Request permission

Erratum: Proc. Amer. Math. Soc. 136 (2008), 3729-3731.

Abstract:

We prove that if the Vietoris hyperspace $CL(X)$ of all nonempty 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 $CL(X)$ is not Baire. This settles an open problem of R. A. McCoy stated in 1975.

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