The Strict Topology in a Completely Regular Setting: Relations to Topological Measure Theory

Mosiman, Steven E. ; Wheeler, Robert F.

Canadian journal of mathematics, Tome 24 (1972) no. 5, pp. 873-890

Résumé

Let X be a locally compact Hausdorff space, and let C* (X) denote the space of real-valued bounded continuous functions on X. An interesting and important property of the strict topology β on C* (X) was proved by Buck [2]: the dual space of (C* (X), β) has a natural representation as the space of bounded regular Borel measures on X.Now suppose that X is completely regular (all topological spaces are assumed to be Hausdorff in this paper). Again it seems natural to seek locally convex topologies on the space C* (X) whose dual spaces are (via the integration pairing) significant classes of measures.

Détail

DOI : 10.4153/CJM-1972-087-2

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