Cao, JGarcia Ferreira, SGutev, V2011-11-112012-05-232012-05-232011-11-112012-05-232012-05-2320072007Proceedings of the American Mathematical Society, vol.135(1), pp.299 - 303 (5)0002-99391088-6826https://hdl.handle.net/10292/4243We 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 whose Vietoris hyperspace CL(X) is not Baire. This settles an open problem of R. A. McCoy stated in 1975.Copyright 2006, American Mathematical Society. This is an Open Access Journal. Authors retain the right to place his/her publication version of the work on a personal website or institutional repository for non commercial purposes. The definitive version was published in (see Citation). The original publication is available at (see Publisher’s Version).Baire spaceProduct spaceHyperspaceVietoris topologyVolterra spaceJournal ArticleOpenAccess10.1090/S0002-9939-06-08743-09702