Completeness Properties of the Generalized Compact-Open Topology of Partial Functions with Closed 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 primary goal of the paper is to investigate the Baire property and weak a-favorability for the generalized compact-open topology tC on the space P of continuous partial functions f :A ? Y with a closed domain A ? X. Various sufficient and necessary conditions are given. It is shown, e.g.,that (P, tC) is weakly a-favorable (and hence a Baire space), if X is a locally compact paracompact space and Y is a regular space having a completely metrizable dense subspace. As corollaries we get sufficient conditions for Baireness and weak a-favorability of the graph topology of Brandi and Ceppitelli introduced for applications in differential equations, as well as of the Fell hyperspace topology. The relationship between tC, the compact-open and Fell topologies, respectively is studied; moreover, a topological game is introduced and studied in order to facilitate the exposition of the above results.

Additional Information

Topology and Its Applications Vol 110, Issue 3
Language: English
Date: 2001
Generalized compact-open topology; Fell topology; Compact-open topology; Topological games; Banach–Mazur game; Weakly a-favorable spaces; Baire spaces; Graph topology; p-base; Restriction mapping

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