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Keywords:
set-valued mapping; lower semi-continuous; upper semi-continuous; selection; countable-dimensional space
set-valued mapping; lower semi-continuous; upper semi-continuous; selection; countable-dimensional space
Summary:
Every l.s.c\. mapping from a paracompact space into the non-empty, closed, convex subsets of a (not necessarily convex) $G_\delta $-subset of a Banach space admits a single-valued continuous selection provided every such mapping admits a convex-valued usco selection. This leads us to some new partial solutions of a problem raised by E. Michael.
References:
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