Geodesic
Nonnormality points of $\beta X \setminus X$
William Fleissner1 ; Lynne Yengulalp2
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

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
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

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. 
@article{10_4064_fm214_3_4,
     author = {William Fleissner and Lynne Yengulalp},
     title = {Nonnormality points of $\beta X \setminus X$},
     journal = {Fundamenta Mathematicae},
     pages = {269--283},
     publisher = {mathdoc},
     volume = {214},
     number = {3},
     year = {2011},
     doi = {10.4064/fm214-3-4},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/fm214-3-4/}
}
TY  - JOUR
AU  - William Fleissner
AU  - Lynne Yengulalp
TI  - Nonnormality points of $\beta X \setminus X$
JO  - Fundamenta Mathematicae
PY  - 2011
SP  - 269
EP  - 283
VL  - 214
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4064/fm214-3-4/
DO  - 10.4064/fm214-3-4
LA  - en
ID  - 10_4064_fm214_3_4
ER  - 
%0 Journal Article
%A William Fleissner
%A Lynne Yengulalp
%T Nonnormality points of $\beta X \setminus X$
%J Fundamenta Mathematicae
%D 2011
%P 269-283
%V 214
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4064/fm214-3-4/
%R 10.4064/fm214-3-4
%G en
%F 10_4064_fm214_3_4
William Fleissner; Lynne Yengulalp. Nonnormality points of $\beta X \setminus X$. Fundamenta Mathematicae, Tome 214 (2011) no. 3, pp. 269-283. doi: 10.4064/fm214-3-4

Cité par Sources :