On Upper Dini’s Systems and U.S.C. Functions With Convex Limit Sets

We give an answer to the question in [HN] as to which upper Dini's systems of functions induces a Hausdorff metric topology on $U_0(X)$. We show that if $X$ is a locally connected metric space then the Hausdorff metric topology on $U_0(X)$ induces as an upper Dini's system of functions the...

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Bibliographic Details
Published inSarajevo journal of mathematics Vol. 2; no. 2; pp. 231 - 236
Main Authors Vuković, Mirjana, Holý, Dušan, Matejička, Ladislav
Format Journal Article
LanguageEnglish
Published 12.06.2024
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Summary:We give an answer to the question in [HN] as to which upper Dini's systems of functions induces a Hausdorff metric topology on $U_0(X)$. We show that if $X$ is a locally connected metric space then the Hausdorff metric topology on $U_0(X)$ induces as an upper Dini's system of functions the set of all bounded upper semicontinuous functions vanishing at infinity with convex limit sets.   2000 Mathematics Subject Classification. Primary: 54C35; secondary: 54C60
ISSN:1840-0655
2233-1964
DOI:10.5644/SJM.02.2.10