Continuous selections and finite-dimensional sets
Ernest Michael · Pacific Journal of Mathematics · 1980
Some known selection theorems are strengthened by weakening the hypotheses on a finite-dimensional subset of the domain.1* Introduction• The following selection theorem was recently obtained in [7] by C. Pixley and the author.THEOREM 1.1.Let X be paracompact, Y a Banach space, ZaX with dim A i? ^r(Y) l.s.c. with φ(x) convex for all x e X -Z.Then φ has a selection.