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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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References:
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