A unified theorem on continuous selections
Ernest Michael, Carl P. Pixley · Pacific Journal of Mathematics · 1980
A selection theorem is proved which unifies and generalizes some known results.l Introduction* The purpose of this note is to prove the following theorem, which unifies and generalizes previously known results.THEOREM 1.1.Let X be paracompact, Y a Banach space, ZaX with άim x Z^0, and φ:X->^(Y) l.s.c. with φ{x) convex for all x e X -Z.Then φ admits a selection.