Generalized selection theorems without convexity

Liang-Ju Chu, Chien Hao Huang

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

In this paper, we extend new selection theorems for almost lower semicontinuous multifunctions T on a paracompact topological space X to general nonconvex settings. On the basis of the KimLee theorem and the Horvath selection theorem, we first show that any a.l.s.c. C-valued multifunction admits a continuous selection under a mild condition of a one-point extension property. Finally, we apply a fundamental selection theorem, due to Ben-El-Mechaiekh and Oudadess, to modify our selection theorems by adjusting a closed subset Z of X with its covering dimension dimXZ≤0. The results derived here generalize and unify various earlier ones from classic continuous selection theory.

Original languageEnglish
Pages (from-to)3224-3231
Number of pages8
JournalNonlinear Analysis, Theory, Methods and Applications
Volume73
Issue number10
DOIs
Publication statusPublished - 2010 Nov 15

Keywords

  • -approximate selection
  • Almost lower semicontinuous
  • C-set
  • C-space
  • Continuous selection
  • Equicontinuous property (ECP)
  • LC-metric space
  • Lower semicontinuous
  • One-point extension property

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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