Baire spaces and Vietoris hyperspaces

Cao, J; Garcia Ferreira, S; Gutev, V

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

Cao, J; Garcia Ferreira, S; Gutev, V

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 whose Vietoris hyperspace CL(X) is not Baire. This settles an open problem of R. A. McCoy stated in 1975.

Keywords

Baire space; Product space; Hyperspace; Vietoris topology; Volterra space

Date

2007

Source

Proceedings of the American Mathematical Society, vol.135(1), pp.299 - 303 (5)

Item Type

Journal Article

Publisher

The American Mathematical Society

DOI

10.1090/S0002-9939-06-08743-0

Publisher's Version

http://dx.doi.org/10.1090/S0002-9939-06-08743-0

Rights Statement

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).