Nonnormality points of $\beta X \setminus X$
Volume 214 / 2011
Fundamenta Mathematicae 214 (2011), 269-283
MSC: Primary 54D80; Secondary 03E45.
DOI: 10.4064/fm214-3-4
Abstract
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.
