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

DOI:
https://doi.org/10.1090/S0002-9939-1987-0870777-3

MathSciNet review:
870777

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Abstract | References | Similar Articles | Additional Information

Abstract: Let denote a locally compact Hausdorff space and the algebra of continuous complex-valued functions on . The main result of this paper is that is paracompact if and only if , the subalgebra of consisting of functions which vanish at infinity, has an approximate identity which is a relatively compact subset of for the weak topology of the pairing of with its strict topology dual.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1987-0870777-3

Keywords:
Approximate identity,
paracompact,
weakly compact

Article copyright:
© Copyright 1987
American Mathematical Society