On non-normality points and metrizable crowded spaces

Sergei Logunov

Commentationes Mathematicae Universitatis Carolinae (2007)

  • Volume: 48, Issue: 3, page 523-527
  • ISSN: 0010-2628

Abstract

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β X - { p } is non-normal for any metrizable crowded space X and an arbitrary point p X * .

How to cite

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Logunov, Sergei. "On non-normality points and metrizable crowded spaces." Commentationes Mathematicae Universitatis Carolinae 48.3 (2007): 523-527. <http://eudml.org/doc/250238>.

@article{Logunov2007,
abstract = {$\beta X-\lbrace p\rbrace $ is non-normal for any metrizable crowded space $X$ and an arbitrary point $p\in X^\{*\}$.},
author = {Logunov, Sergei},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {nice family; $p$-filter; $p$-ultrafilter; projection; non-normality point; butterfly-point; nice family; -filter; -ultrafilter; projection; non-normality point; butterfly-point},
language = {eng},
number = {3},
pages = {523-527},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On non-normality points and metrizable crowded spaces},
url = {http://eudml.org/doc/250238},
volume = {48},
year = {2007},
}

TY - JOUR
AU - Logunov, Sergei
TI - On non-normality points and metrizable crowded spaces
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2007
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 48
IS - 3
SP - 523
EP - 527
AB - $\beta X-\lbrace p\rbrace $ is non-normal for any metrizable crowded space $X$ and an arbitrary point $p\in X^{*}$.
LA - eng
KW - nice family; $p$-filter; $p$-ultrafilter; projection; non-normality point; butterfly-point; nice family; -filter; -ultrafilter; projection; non-normality point; butterfly-point
UR - http://eudml.org/doc/250238
ER -

References

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  1. Blaszczyk A., Szymanski A., Some nonnormal subspaces of the Čech-Stone compactifications of a discrete space, in: Proc. 8-th Winter School on Abstract Analysis, Prague, 1980. 
  2. Gryzlov A.A., On the question of hereditary normality of the space β ø m e g a ø m e g a , (1982), Topology and Set Theory (Udmurt. Gos. Univ., Izhevsk) 61-64 (in Russian). (1982) MR0760274
  3. Logunov S., On hereditary normality of compactifications, Topology Appl. (1996), 73 213-216. (1996) Zbl0869.54029MR1419794
  4. Logunov S., On hereditary normality of zero-dimensional spaces, Topology Appl. (2000), 102 53-58. (2000) Zbl0944.54016MR1739263
  5. Logunov S., On remote points, non-normality and π -weight ø m e g a 1 , Comment. Math. Univ. Carolin. (2001), 42 2 379-384. (2001) Zbl1053.54031MR1832156
  6. Logunov S., On remote points and butterfly-points, (2002), 3 (26) Izvestia instituta matematiki i informatiki, Udmurt State University, Izhevsk (in Russian) 115-120. (2002) 
  7. van Mill J., An easy proof that β N N { p } is non-normal, Ann. Math. Silesianea (1984), 2 81-84. (1984) 
  8. Rajagopalan M., β N N { p } is not normal, J. Indian Math. Soc. (1972), 36 173-176. (1972) MR0321012
  9. Shapirovskij B., On embedding extremely disconnected spaces in compact Hausdorff spaces, b -points and weight of pointwise normal spaces, Dokl. Akad. Nauk SSSR (1975), 223 1083-1086. (1975) MR0394609
  10. Terasawa J., On the non-normality of β X - { p } for non-discrete spaces X , Topology Proc. (2003), 27 335-344. (2003) MR2048942

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