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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Approximate identities and paracompactness
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by R. A. Fontenot and R. F. Wheeler PDF
Proc. Amer. Math. Soc. 99 (1987), 232-236 Request permission

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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Additional Information
  • © Copyright 1987 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 99 (1987), 232-236
  • MSC: Primary 46J10; Secondary 46E25, 54D18
  • DOI: https://doi.org/10.1090/S0002-9939-1987-0870777-3
  • MathSciNet review: 870777