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A generalization of the strict topology

1971
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Transactions of the American Mathematical Society
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The strict topology ß on the space C(X) of bounded real-valued continuous functions on a topological space X was defined, for locally compact X, by Buck (Michigan Math. J. 5 (1958), 95-104). Among other things he showed that (a) C(X) is /3-complete, (b) the dual of C(X) under the strict topology is the space of all finite signed regular Borel measures on X, and (c) a Stone-Weierstrass theorem holds for /¡-closed subalgebras of C(X). In this paper the definition of the strict topology is

doi:10.1090/s0002-9947-1971-0282206-4
fatcat:5prxqkkl4vh7hfw5sqqz65t4ti