Vietoris topology on partial maps with compact domains

UNCP Author/Contributor (non-UNCP co-authors, if there are any, appear on document)
Dr. Laszlo Zsilinszky, Professor (Creator)
The University of North Carolina at Pembroke (UNCP )
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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 Cech-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).

Additional Information

Topology and Its Applications Vol. 157, Issue 8
Language: English
Date: 2010
Partial maps, Vietoris topology (Generalized) compact-open topology, Completeness properties, Banach–Mazur game, Strong Choquet game (Hereditarily), Baire spaces

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