Properties of Stone-Čech compactifications of discrete spaces

Warren, Nancy M.

doi:10.1090/S0002-9939-1972-0292035-X

Properties of Stone-Čech compactifications of discrete spaces
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Proc. Amer. Math. Soc. 33 (1972), 599-606 Request permission

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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Ensembles linéaires et une classe de tableaux ramifiés

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