Baire spaces, Tychonoff powers and the Vietoris topology |
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| Authors: | Jiling Cao A. H. Tomita |
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| Affiliation: | School of Mathematical Sciences, Auckland University of Technology, Private Bag 92006, Auckland 1020, New Zealand ; Departamento de Matemática, Institute of Mathematics and Statistics, University of São Paulo, 05315 São Paulo, Brazil |
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| Abstract: | In this paper, we show that if the Tychonoff power  of a quasi-regular space  is Baire, then its Vietoris hyperspace  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. |
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| Keywords: | Baire space Choquet game Tychonoff power Vietoris topology. |
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