Baire spaces and Vietoris hyperspaces

Date
2007
Authors
Cao, J
Garcia Ferreira, S
Gutev, V
Supervisor
Item type
Journal Article
Degree name
Journal Title
Journal ISSN
Volume Title
Publisher
The American Mathematical Society
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.

Description
Keywords
Baire space , Product space , Hyperspace , Vietoris topology , Volterra space
Source
Proceedings of the American Mathematical Society, vol.135(1), pp.299 - 303 (5)
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).