Vol. 43, No. 1, 1972

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Approximate identities and the strict topology

Heron S. Collins and Robert A. Fontenot

Vol. 43 (1972), No. 1, 63–79

This paper studies relationships between approximate identities on a B algebra A and other properties of the algebra. If A is commutative, conditions on the approximate identity for A are related to topological properties of the spectrum of A. The principal result of this paper is that for a locally compacl Hausdorff space S,C0(S) has an approximate identity that is totally bounded in the strict topology (or compact open topology) if and only if S is paracompact.

Mathematical Subject Classification 2000
Primary: 46K05
Received: 1 June 1971
Published: 1 October 1972
Heron S. Collins
Robert A. Fontenot