A generalization of the strict topology

Author:
Robin Giles

Journal:
Trans. Amer. Math. Soc. **161** (1971), 467-474

MSC:
Primary 46.25

MathSciNet review:
0282206

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Abstract: The strict topology on the space 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) is -complete, (b) the dual of 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 . In this paper the definition of the strict topology is generalized to cover the case of an arbitrary topological space and these results are established under the following conditions on *X*: for (a) *X* is a *k*-space; for (b) *X* is completely regular; for (c) *X* is unrestricted.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1971-0282206-4

Keywords:
Strict topology,
Stone-Weierstrass theorem,
completely regular space,
*k*-space,
regular Borel measure

Article copyright:
© Copyright 1971
American Mathematical Society