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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)


Topologies on spaces of vector-valued continuous functions

Author: Surjit Singh Khurana
Journal: Trans. Amer. Math. Soc. 241 (1978), 195-211
MSC: Primary 46E40; Secondary 58D15
MathSciNet review: 492297
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Abstract: Topologies $ {\beta _0},{\beta _1},\beta ,{\beta _\infty },{\beta _{\infty c}}$ are defined on $ {C_b}(X,E)$, the space of all bounded, continuous functions from a completely regular Hausdorff space X, into E, a normed space, and their duals are determined. Also many properties of these topologies are proved.

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PII: S 0002-9947(1978)0492297-X
Keywords: $ \tau $-smooth measures, tight measures, Dunford-Pettis property, Mackey topology, strict topologies, vector-valued functions and measures
Article copyright: © Copyright 1978 American Mathematical Society