Fell topology on the space of functions with closed graph

descriptionPublicationkeyboard_double_arrow_right Article 01 Oct 1999 English Publisher:Springer Science and Business Media LLCJournal:Rendiconti del Circolo Matematico di Palermo, volume 48, pages 419-430 (issn: 0009-725X, eissn: 1973-4409,

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Authors: Holá, Ľ.; Poppe, H.;

doi: 10.1007/bf02844333

Fell topology on the space of functions with closed graph

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Abstract

This paper studies the Fell topology on the space \(G(X,Y)\) of all functions from \(X\) into \(Y\) that have closed graphs. The topology on this space is compared to other topologies, including the compact-open topology and those of Kuratowski convergence and continuous convergence. Characterizations are given for separation properties, countability properties and metrizability of \(G(X,R)\) in terms of properties of \(X\).

Related Organizations

University of Rostock
Germany
Slovak Academy of Sciences
Slovakia

Keywords

Fell topology, Function spaces in general topology, function with a closed graph, Hyperspaces in general topology, locally compact space, compact-open topology

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