# Concepts of lower semicontinuity and continuous selections for convex valued multifunctions

@article{Przeawski1992ConceptsOL,
title={Concepts of lower semicontinuity and continuous selections for convex valued multifunctions},
author={Krzysztof Przeławski and Longin E. Rybiński},
journal={Journal of Approximation Theory},
year={1992},
volume={68},
pages={262-282}
}
• Published 1 March 1992
• Mathematics
• Journal of Approximation Theory
14 Citations
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Let $({\mathcal M},\rho)$ be a metric space and let $Y$ be a Banach space. Given a positive integer $m$, let $F$ be a set-valued mapping from ${\mathcal M}$ into the family of all compact convex
Michael's Selection Theorem under an Assumption Weaker than Lower Semicontinuous in H-spaces
A new continuous selection theorem is proved which unifies and generalizes some known results.
Bicommutants of multiplication operators
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LetM = (M, ρ) be a metric space and let X be a Banach space. Let F be a setvalued mapping fromM into the family Km(X) of all compact convex subsets of X of dimension at most m. The main result in our

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Two new continuity properties for set-valued mappings are defined which are weaker than lower semicontinuity. One of these properties characterizes when approximate selections exist. A few selection