Non-normality points and nice spaces

Sergei Logunov

Commentationes Mathematicae Universitatis Carolinae (2021)

  • Volume: 62, Issue: 3, page 383-392
  • ISSN: 0010-2628

Abstract

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J. Terasawa in " β X - { p } are non-normal for non-discrete spaces X " (2007) and the author in “On non-normality points and metrizable crowded spaces” (2007), independently showed for any metrizable crowded space X that each point p of its Čech–Stone remainder X * is a non-normality point of β X . We introduce a new class of spaces, named nice spaces, which contains both of Sorgenfrey line and every metrizable crowded space. We obtain the result above for every nice space.

How to cite

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Logunov, Sergei. "Non-normality points and nice spaces." Commentationes Mathematicae Universitatis Carolinae 62.3 (2021): 383-392. <http://eudml.org/doc/297976>.

@article{Logunov2021,
abstract = {J. Terasawa in "$\beta X-\lbrace p\rbrace $ are non-normal for non-discrete spaces $X$" (2007) and the author in “On non-normality points and metrizable crowded spaces” (2007), independently showed for any metrizable crowded space $X$ that each point $p$ of its Čech–Stone remainder $X^\{*\}$ is a non-normality point of $\beta X$. We introduce a new class of spaces, named nice spaces, which contains both of Sorgenfrey line and every metrizable crowded space. We obtain the result above for every nice space.},
author = {Logunov, Sergei},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {non-normality point; butterfly-point; nice family; nice space; metrizable crowded space; Sorgenfrey line},
language = {eng},
number = {3},
pages = {383-392},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Non-normality points and nice spaces},
url = {http://eudml.org/doc/297976},
volume = {62},
year = {2021},
}

TY - JOUR
AU - Logunov, Sergei
TI - Non-normality points and nice spaces
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2021
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 62
IS - 3
SP - 383
EP - 392
AB - J. Terasawa in "$\beta X-\lbrace p\rbrace $ are non-normal for non-discrete spaces $X$" (2007) and the author in “On non-normality points and metrizable crowded spaces” (2007), independently showed for any metrizable crowded space $X$ that each point $p$ of its Čech–Stone remainder $X^{*}$ is a non-normality point of $\beta X$. We introduce a new class of spaces, named nice spaces, which contains both of Sorgenfrey line and every metrizable crowded space. We obtain the result above for every nice space.
LA - eng
KW - non-normality point; butterfly-point; nice family; nice space; metrizable crowded space; Sorgenfrey line
UR - http://eudml.org/doc/297976
ER -

References

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  1. Błaszczyk A., Szymański A., Some non-normal subspaces of the Čech–Stone compactification of a discrete space, in Abstracta, 8th Winter School on Abstract Analysis, Czechoslovak Academy of Sciences, Praha, 1980, pages 35–38. 
  2. Logunov S., 10.1016/S0166-8641(96)00063-6, Topology Appl. 73 (1996), no. 3, 213–216. DOI10.1016/S0166-8641(96)00063-6
  3. Logunov S., 10.1016/S0166-8641(98)00137-0, Topology Appl. 102 (2000), no. 1, 53–58. DOI10.1016/S0166-8641(98)00137-0
  4. Logunov S., On remote points, non-normality and π -weight ω 1 , Comment. Math. Univ. Carolin. 42 (2001), no. 2, 379–384. 
  5. Logunov S., On non-normality points and metrizable crowded spaces, Comment. Math. Univ. Carolin. 48 (2007), no. 3, 523–527. 
  6. Logunov S., Non-normality points and big products of metrizable spaces, Topology Proc. 46 (2015), 73–85. 
  7. Šapirovskiĭ B. È., The embedding of extremely disconnected spaces in bicompacta. b-points and weight of point-wise normal spaces, Dokl. Akad. Nauk SSSR 223 (1975), no. 5, 1083–1086 (Russian). 
  8. Terasawa J., β X - { p } are non-normal for non-discrete spaces X , Topology Proc. 31 (2007), no. 1, 309–317. 
  9. Warren N. M., Properties of Stone–Čech compactifications of discrete spaces, Proc. Amer. Math. Soc. 33 (1972), 599–606. 

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