Abstract:
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].