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Baire spaces and Vietoris hyperspaces |
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| Authors: | Jiling Cao Salvador Garcí a-Ferreira Valentin Gutev |
| Affiliation: | Department of Mathematics, The University of Auckland, Private Bag 92019, Auckland 1, New Zealand ; Instituto de Matematicas (UNAM), Apartado Postal 61-3, Xangari 58089, Morelia, Michoacan, Mexico ; School of Mathematical Sciences, Faculty of Science, University of KwaZulu-Natal, King George V Avenue, Durban 4041, South Africa |
| Abstract: | We prove that if the Vietoris hyperspace  of all nonempty closed subsets of a space  is Baire, then all finite powers of  must be Baire spaces. In particular, there exists a metrizable Baire space  whose Vietoris hyperspace  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 |
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