Displaying similar documents to “A selection theorem for open-graph multifunctions”

Closed graph multi-selections

Valentin Gutev (2011)

Fundamenta Mathematicae

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A classical Lefschetz result about point-finite open covers of normal spaces is generalised by showing that every lower semi-continuous mapping from a normal space into the nonempty compact subsets of a metrizable space admits a closed graph multi-selection. Several applications are given as well.

Relations approximated by continuous functions in the Vietoris topology

L'. Holá, R. A. McCoy (2007)

Fundamenta Mathematicae

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Let X be a Tikhonov space, C(X) be the space of all continuous real-valued functions defined on X, and CL(X×ℝ) be the hyperspace of all nonempty closed subsets of X×ℝ. We prove the following result: Let X be a locally connected locally compact paracompact space, and let F ∈ CL(X×ℝ). Then F is in the closure of C(X) in CL(X×ℝ) with the Vietoris topology if and only if: (1) for every x ∈ X, F(x) is nonempty; (2) for every x ∈ X, F(x) is connected; (3) for every isolated x ∈ X, F(x) is...

On multifunctions with closed graphs

D. Holý (2001)

Mathematica Bohemica

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The set of points of upper semicontinuity of multi-valued mappings with a closed graph is studied. A topology on the space of multi-valued mappings with a closed graph is introduced.