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Properties of Stone-Čech compactifications of discrete spaces

Author: Nancy M. Warren
Journal: Proc. Amer. Math. Soc. 33 (1972), 599-606
MSC: Primary 54D35
MathSciNet review: 0292035
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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$.

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Keywords: Stone-Čech compactification, P-point, $ {C^\ast}$-embedding, discrete spaces
Article copyright: © Copyright 1972 American Mathematical Society

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