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http://dx.doi.org/10.5831/HMJ.2013.35.4.757

A MISCELLANY OF SELECTION THEOREMS WITHOUT CONVEXITY  

Kim, Hoonjoo (Department of mathematics education, Sehan University)
Publication Information
Honam Mathematical Journal / v.35, no.4, 2013 , pp. 757-764 More about this Journal
Abstract
In this paper, we give sufficient conditions for a map with nonconvex values to have a continuous selection and the selection extension property in LC-metric spaces under the one-point extension property. And we apply it to weakly lower semicontinuous maps and generalize previous results. We also get a continuous selection theorem for almost lower semicontinuous maps with closed sub-admissible values in $\mathbb{R}$-trees.
Keywords
selection; LC-metric space; weakly lower semicontinuous; quasi-lower semicontinuous; almost lower semicontinuous; one-point extension property; selection extension; hyperconvex; R-tree;
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