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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Vector-valued continuous functions with strict topologies and angelic topological spaces


Author: Surjit Singh Khurana
Journal: Proc. Amer. Math. Soc. 69 (1978), 34-36
MSC: Primary 46E40
DOI: https://doi.org/10.1090/S0002-9939-1978-0493313-7
MathSciNet review: 0493313
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Abstract: It is proved that if X is a metric space, E a Banach space containing a $ \sigma $-weakly-compact dense subset, then the space $ ({M_\tau }(X,E'),\sigma ({M_\tau }(X,E'),{C_b}(X,E)))$ is angelic, $ {C_b}(X,E)$ being all bounded continuous functions from X into E and $ {M_\tau }(X,E')$ the dual of $ {C_b}(X,E)$ with the strict topology $ \beta $.


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DOI: https://doi.org/10.1090/S0002-9939-1978-0493313-7
Article copyright: © Copyright 1978 American Mathematical Society