Lindelöf property in function spaces and a related selection theorem

Author:
Witold Marciszewski

Journal:
Proc. Amer. Math. Soc. **101** (1987), 545-550

MSC:
Primary 54C35; Secondary 46E25, 54C65

DOI:
https://doi.org/10.1090/S0002-9939-1987-0908666-8

MathSciNet review:
908666

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Abstract: Let be a separable metrizable space. If is a compact space whose function space is weakly -analytic, then the space of continuous maps from to with the pointwise topology has the Lindelöf property. If is a Banach space whose weak topology is -analytic, then each lower semicontinuous map from to the family of nonempty closed convex subsets of the unit ball of the dual with the weak*-topology admits a continuous selection. This extends some results of Corson and Lindenstrauss.

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DOI:
https://doi.org/10.1090/S0002-9939-1987-0908666-8

Article copyright:
© Copyright 1987
American Mathematical Society