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)

 

 

Properties of Stone-Čech compactifications of discrete spaces


Author: Nancy M. Warren
Journal: Proc. Amer. Math. Soc. 33 (1972), 599-606
MSC: Primary 54D35
DOI: https://doi.org/10.1090/S0002-9939-1972-0292035-X
MathSciNet review: 0292035
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ \beta N$ be the Stone-Čech compactification of the integers N. It is shown that p is a P-point of $ \beta N - N$, then $ \beta N - N - \{ p\} $ is not normal. Let D be an uncountable discrete set and $ {E_0}$ be the set of points in $ \beta D - D$ in the closures of countable subsets of D It is shown that there is a two-valued continuous function on $ {E_0}$ which cannot be extended continuously to $ \beta D$.


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


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 54D35

Retrieve articles in all journals with MSC: 54D35


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0292035-X
Keywords: Stone-Čech compactification, P-point, $ {C^\ast}$-embedding, discrete spaces
Article copyright: © Copyright 1972 American Mathematical Society