Nonnormality points of $\beta X \setminus X$

Volume 214 / 2011

William Fleissner, Lynne Yengulalp 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.

Authors

  • William FleissnerDepartment of Mathematics
    University of Kansas
    Lawrence, KS 66045, U.S.A.
    e-mail
  • Lynne YengulalpDepartment of Mathematics
    University of Dayton
    Dayton, OH 45469, U.S.A.
    e-mail

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