Vietoris topology on partial maps with compact domains |
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Authors: | L'ubica Holá ,Lá szló Zsilinszky |
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Affiliation: | a Academy of Sciences, Institute of Mathematics, Štefánikova 49, 81473 Bratislava, Slovakia b Department of Mathematics and Computer Science, University of North Carolina at Pembroke, Pembroke, NC 28372, USA |
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Abstract: | The space PK 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 PK, including ?ech-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). |
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Keywords: | primary, 54B20 secondary, 54C35 |
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