Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The strict topology $ \beta $ 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 $ \beta $-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 $ \beta $-closed subalgebras of $ C(X)$. 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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 46.25

Retrieve articles in all journals with MSC: 46.25


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1971-0282206-4
PII: S 0002-9947(1971)0282206-4
Keywords: Strict topology, Stone-Weierstrass theorem, completely regular space, k-space, regular Borel measure
Article copyright: © Copyright 1971 American Mathematical Society