On hereditary normality of ω * , Kunen points and character ω 1

Sergei Logunov

Commentationes Mathematicae Universitatis Carolinae (2021)

  • Volume: 62, Issue: 4, page 507-511
  • ISSN: 0010-2628

Abstract

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We show that ω * ∖ { p } is not normal, if p is a limit point of some countable subset of ω * , consisting of points of character ω 1 . Moreover, such a point p is a Kunen point and a super Kunen point.

How to cite

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Logunov, Sergei. "On hereditary normality of $\omega ^*$, Kunen points and character $\omega _{1}$." Commentationes Mathematicae Universitatis Carolinae 62.4 (2021): 507-511. <http://eudml.org/doc/297996>.

@article{Logunov2021,
abstract = {We show that $\omega ^\{*\}\setminus \lbrace p\rbrace $ is not normal, if $p$ is a limit point of some countable subset of $\omega ^\{*\}$, consisting of points of character $\omega _\{1\}$. Moreover, such a point $p$ is a Kunen point and a super Kunen point.},
author = {Logunov, Sergei},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {non-normality point; butterfly point; Kunen point; super Kunen point},
language = {eng},
number = {4},
pages = {507-511},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On hereditary normality of $\omega ^*$, Kunen points and character $\omega _\{1\}$},
url = {http://eudml.org/doc/297996},
volume = {62},
year = {2021},
}

TY - JOUR
AU - Logunov, Sergei
TI - On hereditary normality of $\omega ^*$, Kunen points and character $\omega _{1}$
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2021
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 62
IS - 4
SP - 507
EP - 511
AB - We show that $\omega ^{*}\setminus \lbrace p\rbrace $ is not normal, if $p$ is a limit point of some countable subset of $\omega ^{*}$, consisting of points of character $\omega _{1}$. Moreover, such a point $p$ is a Kunen point and a super Kunen point.
LA - eng
KW - non-normality point; butterfly point; Kunen point; super Kunen point
UR - http://eudml.org/doc/297996
ER -

References

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  1. Bešlagić A., van Douwen E. K., 10.1016/0166-8641(90)90110-N, Topology Appl. 35 (1990), no. 2–3, 253–260. MR1058805DOI10.1016/0166-8641(90)90110-N
  2. Błaszczyk A., Szymański A., Some non-normal subspaces of the Čech–Stone compactification of a discrete space, Proc. Eighth Winter School on Abstract Analysis, Czechoslovak Academy of Sciences, Praha, 1980, pages 35–38. 
  3. Comfort W. W., Negrepontis S., 10.1007/BF01111048, Math. Z. 107 (1968), 53–58. MR0234422DOI10.1007/BF01111048
  4. Fine N. J., Gillman L., 10.1090/S0002-9904-1960-10460-0, Bull. Amer. Math. Soc. 66 (1960), 376–381. MR0123291DOI10.1090/S0002-9904-1960-10460-0
  5. Gryzlov A. A., On the question of hereditary normality of the space β ω ∖ ω , Topology and Set Theory, Udmurt. Gos. Univ., Izhevsk, 1982, 61–64 (Russian). MR0760274
  6. Rajagopalan M., β N - N - { p } is not normal, J. Indian Math. Soc. (N.S.) 36 (1972), 173–176. MR0321012
  7. Szymanski A., Retracts and non-normality points, Topology Proc. 40 (2012), 195–201. MR2832067
  8. Warren N. M., Properties of Stone–Čech compactifications of discrete spaces, Proc. Amer. Math. Soc. 33 (1972), 599–606. MR0292035

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