An example concerning continuous selections of infinite-dimensional spaces

Pixley, Carl P.

doi:10.1090/S0002-9939-1974-0328858-X

An example concerning continuous selections of infinite-dimensional spaces

Author: Carl P. Pixley
Journal: Proc. Amer. Math. Soc. 43 (1974), 237-244
MSC: Primary 54C65
DOI: https://doi.org/10.1090/S0002-9939-1974-0328858-X
MathSciNet review: 0328858
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Abstract: This paper shows that the conclusion of E. Michael's Selection Theorem 1.2 [Continuous selections. II, Ann. of Math. (2) 64 (1956), 562-580. MR 18, 325.] does not necessarily hold if the hypotheses are modified by dropping the assumption that the domain of the lsc carrier is of finite dimension, and strengthening the equilocal and global mapping conditions on the collection of images under the carrier.

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