Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

The essential closure of $ C(X)$


Author: Marlow Anderson
Journal: Proc. Amer. Math. Soc. 76 (1979), 8-10
MSC: Primary 06F15; Secondary 54C40
MathSciNet review: 534378
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Each archimedean l-group admits a unique essential closure, which is the l-group of continuous almost finite real-valued functions on some Stonean space; thus the l-group $ C(X)$ of real-valued continuous functions on a topological space X admits such an essential closure. In this note we will construct a natural embedding of $ C(X)$ into its essential closure, making explicit the topological relationship between X and the appropriate Stonean space.


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


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 06F15, 54C40

Retrieve articles in all journals with MSC: 06F15, 54C40


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1979-0534378-4
Article copyright: © Copyright 1979 American Mathematical Society