Proceedings of the American Mathematical Society

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



Approximate identities and paracompactness

Authors: R. A. Fontenot and R. F. Wheeler
Journal: Proc. Amer. Math. Soc. 99 (1987), 232-236
MSC: Primary 46J10; Secondary 46E25, 54D18
MathSciNet review: 870777
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Abstract: Let $ X$ denote a locally compact Hausdorff space and $ {C_b}(X)$ the algebra of continuous complex-valued functions on $ X$. The main result of this paper is that $ X$ is paracompact if and only if $ {C_0}(X)$, the subalgebra of $ {C_b}(X)$ consisting of functions which vanish at infinity, has an approximate identity which is a relatively compact subset of $ {C_b}(X)$ for the weak topology of the pairing of $ {C_b}(X)$ with its strict topology dual.

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Keywords: Approximate identity, paracompact, weakly compact
Article copyright: © Copyright 1987 American Mathematical Society