Nonnormality points of $\beta X \setminus X$

William Fleissner ¹   ; Lynne Yengulalp ²

¹ Department of Mathematics University of Kansas Lawrence, KS 66045, U.S.A.
² Department of Mathematics University of Dayton Dayton, OH 45469, U.S.A.

Fundamenta Mathematicae, Tome 214 (2011) no. 3, pp. 269-283

Résumé

Let $X$ be a crowded metric space of weight $\def\k{\kappa}\k$ that is either $\def\wk{\k^\omega\text{-like}}\wk$ or locally compact. Let $\def\b{\beta}\def\bs{\setminus}y \in \b X \bs X$ and assume GCH. Then a space of nonuniform ultrafilters embeds as a closed subspace of $\def\b{\beta}\def\bs{\setminus}(\b X \bs X)\bs \{y\}$ with $y$ as the unique limit point. If, in addition, $y$ is a regular $z$-ultrafilter, then the space of nonuniform ultrafilters is not normal, and hence $\def\b{\beta}\def\bs{\setminus}(\b X \bs X)\bs \{y\}$ is not normal.

Détail

DOI : 10.4064/fm214-3-4

Keywords: crowded metric space weight def kappa either def omega text like locally compact def beta def setminus assume gch space nonuniform ultrafilters embeds closed subspace def beta def setminus unique limit point addition regular z ultrafilter space nonuniform ultrafilters normal hence def beta def setminus normal