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
Copyright
Copyright © 2011, Instytut Matematyczny Polskiej Akademii Nauk
Publisher
Instytut Matematyczny Polskiej Akademii Nauk
Volume
214
Issue
3
Peer Reviewed
yes
eCommons Citation
Fleissner, William and Yengulalp, Lynne, "Non-Normality Points of β X\X" (2011). Mathematics Faculty Publications. 38.
https://ecommons.udayton.edu/mth_fac_pub/38
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.