Electronic Version 18 (1993), 189-194

E. Michael

The purpose of this note is to prove the following theorem, which was stated without proof in [5, Theorem 2.9].

Theorem Let Y be metrizable and E a hereditary subset of 2^Y hereditary. Then the following are equivalent.

1. If X is metrizable, then every l.s.c. \phi: X --> E has a selection.
2. If X is metrizable, then every l.s.c. \phi: X --> E is equi-connected and has selections locally.

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volume 18: table of contents
topology proceedings Electronic Version