On Upper Dini’s Systems and U.S.C. Functions With Convex Limit Sets
DOI:
https://doi.org/10.5644/SJM.02.2.10Keywords:
Upper semicontinuous functions, Dini’s systems, Hausdorff metric, convex limit setsAbstract
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
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References
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