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)

 

 

A compactification of locally compact spaces


Author: F. W. Lozier
Journal: Proc. Amer. Math. Soc. 31 (1972), 577-579
DOI: https://doi.org/10.1090/S0002-9939-1972-0286072-9
MathSciNet review: 0286072
Full-text PDF Free Access

Abstract | References | Additional Information

Abstract: Every locally compact space $ X$ has its topology determined by its 1-1 compact images and hence has a compactification $ \xi X$ obtained as the closure of the natural embedding of $ X$ in the product of those images, just as the Stone-Čech compactification $ \beta X$ can be obtained by embedding $ X$ in a product of intervals. The obvious question is whether $ \xi X = \beta X$. In this paper we prove that $ \xi X = \beta X$ if $ X$ either is 0-dimensional or contains an arc, and give an example in which $ \xi X \ne \beta X$.


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


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0286072-9
Keywords: Compactification, Stone-Čech compactification
Article copyright: © Copyright 1972 American Mathematical Society