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Selection theorems under an assumption weaker than lower semi-continuity. (English) Zbl 0809.54015
Summary: Every set-valued mapping satisfying an assumption weaker than lower semi- continuity admits a lower semi-continuous selection. Besides in the selection theory, this result is also successful in solving the problem of extending lower semi-continuous mappings from arbitrary to \(G_ \delta\)-subsets of metric spaces.

MSC:
54C65 Selections in general topology
54C60 Set-valued maps in general topology
54C20 Extension of maps
54E50 Complete metric spaces
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