Vietoris topology on partial maps with compact domains

The space P K of partial maps with compact domains (identified with their graphs) forms a subspace of the hyperspace of nonempty compact subsets of a product space endowed with the Vietoris topology. Various completeness properties of P K , including Čech-completeness, sieve completeness, strong Cho...

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Bibliographic Details
Published inTopology and its applications Vol. 157; no. 8; pp. 1439 - 1447
Main Authors Holá, L'ubica, Zsilinszky, László
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.06.2010
Subjects
(Generalized) compact-open topology
(Hereditarily) Baire spaces
Banach–Mazur game
Completeness properties
Partial maps
Strong Choquet game
Vietoris topology
secondary
Vietoris topology
(Hereditarily) Baire spaces
(Generalized) compact-open topology
Strong Choquet game
Banach–Mazur game
Completeness properties
Partial maps
primary
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Summary:The space P K of partial maps with compact domains (identified with their graphs) forms a subspace of the hyperspace of nonempty compact subsets of a product space endowed with the Vietoris topology. Various completeness properties of P K , including Čech-completeness, sieve completeness, strong Choquetness, and (hereditary) Baireness, are investigated. Some new results on the hyperspace K ( X ) of compact subsets of a Hausdorff X with the Vietoris topology are obtained; in particular, it is shown that there is a strongly Choquet X, with 1st category K ( X ) .
ISSN:0166-8641
1879-3207
DOI:10.1016/j.topol.2009.03.057