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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
MathSciNet review: 908666
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Abstract: Let $ X$ be a separable metrizable space. If $ K$ is a compact space whose function space $ C(K)$ is weakly $ \mathcal{K}$-analytic, then the space $ {C_p}(X,K)$ of continuous maps from $ X$ to $ K$ with the pointwise topology has the Lindelöf property. If $ E$ is a Banach space whose weak topology is $ \mathcal{K}$-analytic, then each lower semicontinuous map from $ X$ to the family of nonempty closed convex subsets of the unit ball of the dual $ E$ with the weak*-topology admits a continuous selection. This extends some results of Corson and Lindenstrauss.

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Article copyright: © Copyright 1987 American Mathematical Society

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