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  •   Open Research
  • AUT Faculties
  • 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, Tychonoff powers and the Vietoris topology

Cao, J; Tomita, AH
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http://hdl.handle.net/10292/2509
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Abstract
In this paper, we show that if the Tychonoff power Xω of a quasiregular space X is Baire, then its Vietoris hyperspace 2X is also Baire. We also provide two examples to show (i) the converse of this result does not hold in general, and (ii) the Baireness of finite powers of a space is insufficient to guarantee the Baireness of its hyperspace.
Keywords
Baire space; Choquet game; Tychonoff power; Vietoris topology
Date
May 5, 2007
Source
Proceedings of the American Mathematical Society, vol.135(5), pp.1565 - 1573
Item Type
Journal Article
Publisher
American Mathematical Society
DOI
10.1090/S0002-9939-07-08855-7
Publisher's Version
http://dx.doi.org/10.1090/S0002-9939-07-08855-7
Rights Statement
Copyright 2007, 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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