Document Type

Article

Publication Date

2011

Publication Source

Fundamenta Mathematicae

Abstract

We seek conditions implying that (β X\X) \ {y} is not normal. Our main theorem: Assume GCH and all uniform ultrafilters are regular. If X is a locally compact metrizable space without isolated points, then (β X\X) \ {y} is not normal for all y ∈ β X\X. In preparing to prove this theorem, we generalize the notions “uniform”, “regular”, and “good” from set ultrafilters to z-ultrafilters. We discuss non-normality points of the product of a discrete space and the real line. We topologically embed a nonstandard real line into the remainder of this product space.

Inclusive pages

269-283

ISBN/ISSN

0016-2736

Document Version

Preprint

Comments

The document available for download is the authors' submitted manuscript, provided in compliance with the publisher's policy on self-archiving. Differences may exist between this document and the published version, which is available using the link provided. Permission documentation is on file.

Publisher

Instytut Matematyczny Polskiej Akademii Nauk

Volume

214

Issue

3

Volume

214

Issue

3

Peer Reviewed

yes

Link to published version

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