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  • Faculty of Design and Creative Technologies (Te Ara Auaha)
  • School of Engineering, Computer and Mathematical Sciences - Te Kura Mātai Pūhanga, Rorohiko, Pāngarau
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Baire spaces and Vietoris hyperspaces

Cao, J; Garcia Ferreira, S; Gutev, V
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http://hdl.handle.net/10292/4243
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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).

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