On remote points, non-normality and π -weight ω 1

Sergei Logunov

Commentationes Mathematicae Universitatis Carolinae (2001)

  • Volume: 42, Issue: 2, page 379-384
  • ISSN: 0010-2628

Abstract

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We show, in particular, that every remote point of X is a nonnormality point of β X if X is a locally compact Lindelöf separable space without isolated points and π w ( X ) ≤ ω 1 .

How to cite

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Logunov, Sergei. "On remote points, non-normality and $\pi $-weight $\omega _1$." Commentationes Mathematicae Universitatis Carolinae 42.2 (2001): 379-384. <http://eudml.org/doc/248771>.

@article{Logunov2001,
abstract = {We show, in particular, that every remote point of $X$ is a nonnormality point of $\beta X$ if $X$ is a locally compact Lindelöf separable space without isolated points and $\pi w(X)\le \omega _\{1\}$.},
author = {Logunov, Sergei},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {remote point; butterfly-point; nonnormality point; remainder; remote point; b-point; non-normality point},
language = {eng},
number = {2},
pages = {379-384},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On remote points, non-normality and $\pi $-weight $\omega _1$},
url = {http://eudml.org/doc/248771},
volume = {42},
year = {2001},
}

TY - JOUR
AU - Logunov, Sergei
TI - On remote points, non-normality and $\pi $-weight $\omega _1$
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2001
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 42
IS - 2
SP - 379
EP - 384
AB - We show, in particular, that every remote point of $X$ is a nonnormality point of $\beta X$ if $X$ is a locally compact Lindelöf separable space without isolated points and $\pi w(X)\le \omega _{1}$.
LA - eng
KW - remote point; butterfly-point; nonnormality point; remainder; remote point; b-point; non-normality point
UR - http://eudml.org/doc/248771
ER -

References

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  1. Blaszczyk A., Szymanski A., Some nonnormal subspaces of the Čech-Stone compactifications of a discrete space, (1980), in: Proc. 8-th Winter School on Abstract Analysis, Prague. (1980) 
  2. Dow A., Remote points in spaces with π -weight ø m e g a 1 , (1984), 124 Fund. Math. (1984) MR0774511
  3. van Douwen E.K., Why certain Čech-Stone remainders are not homogeneous, (1979), 41 Colloq. Math. (1979) Zbl0424.54012MR0550626
  4. van Douwen E.K., Remote points, (1988), 188 Dissert. Math. (1988) 
  5. 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). (1982) MR0760274
  6. Logunov S., On hereditary normality of compactifications, (1996), 73 Topology Appl. (1996) Zbl0869.54029MR1419794
  7. Logunov S., On hereditary normality of zero-dimensional spaces, (2000), 102 Topology Appl. (2000) Zbl0944.54016MR1739263
  8. van Mill J., An easy proof that β N ∖ N ∖ { p } is non-normal, (1984), 2 Ann. Math. Silesianea. (1984) 
  9. Rajagopalan M., β N ∖ N ∖ { p } is not normal, (1972), 36 J. Indian Math. Soc. (1972) MR0321012
  10. Shapirovskij B., On embedding extremely disconnected spaces in compact Hausdorff spaces, b-points and weight of pointwise normal spaces, (1987), 223 Dokl. Akad. Nauk SSSR. (1987) 

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