Aull-paracompactness and strong star-normality of subspaces in topological spaces

Kaori Yamazaki

Commentationes Mathematicae Universitatis Carolinae (2004)

  • Volume: 45, Issue: 4, page 743-747
  • ISSN: 0010-2628

Abstract

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We prove for a subspace Y of a T 1 -space X , Y is (strictly) Aull-paracompact in X and Y is Hausdorff in X if and only if Y is strongly star-normal in X . This result provides affirmative answers to questions of A.V. Arhangel’skii–I.Ju. Gordienko [3] and of A.V. Arhangel’skii [2].

How to cite

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Yamazaki, Kaori. "Aull-paracompactness and strong star-normality of subspaces in topological spaces." Commentationes Mathematicae Universitatis Carolinae 45.4 (2004): 743-747. <http://eudml.org/doc/249377>.

@article{Yamazaki2004,
abstract = {We prove for a subspace $Y$ of a $T_1$-space $X$, $Y$ is (strictly) Aull-paracompact in $X$ and $Y$ is Hausdorff in $X$ if and only if $Y$ is strongly star-normal in $X$. This result provides affirmative answers to questions of A.V. Arhangel’skii–I.Ju. Gordienko [3] and of A.V. Arhangel’skii [2].},
author = {Yamazaki, Kaori},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Aull-paracompactness of $Y$ in $X$; strong star-normality of $Y$ in $X$; Aull-paracompactness of in ; strong star-normality of in ; fully normal space; paracompact space},
language = {eng},
number = {4},
pages = {743-747},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Aull-paracompactness and strong star-normality of subspaces in topological spaces},
url = {http://eudml.org/doc/249377},
volume = {45},
year = {2004},
}

TY - JOUR
AU - Yamazaki, Kaori
TI - Aull-paracompactness and strong star-normality of subspaces in topological spaces
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2004
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 45
IS - 4
SP - 743
EP - 747
AB - We prove for a subspace $Y$ of a $T_1$-space $X$, $Y$ is (strictly) Aull-paracompact in $X$ and $Y$ is Hausdorff in $X$ if and only if $Y$ is strongly star-normal in $X$. This result provides affirmative answers to questions of A.V. Arhangel’skii–I.Ju. Gordienko [3] and of A.V. Arhangel’skii [2].
LA - eng
KW - Aull-paracompactness of $Y$ in $X$; strong star-normality of $Y$ in $X$; Aull-paracompactness of in ; strong star-normality of in ; fully normal space; paracompact space
UR - http://eudml.org/doc/249377
ER -

References

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  1. Arhangel'skii A.V., Relative topological properties and relative topological spaces, Topology Appl. 70 (1996), 87-99. (1996) Zbl0848.54016MR1397067
  2. Arhangel'skii A.V., From classic topological invariants to relative topological properties, Sci. Math. Japon. 55 (2002), 153-201. (2002) MR1885790
  3. Arhangel'skii A.V., Gordienko I.Ju., Relative symmetrizability and metrizability, Comment. Math. Univ. Carolinae 37 (1996), 757-774. (1996) Zbl0886.54001MR1440706
  4. Burke D.K., Covering properties, in: K. Kunen, J.E. Vaughan (eds.), Handbook of Set-Theoretic Topology, North-Holland, Amsterdam, 1984, pp.347-422. Zbl0569.54022MR0776628
  5. Engelking R., General Topology, Heldermann Verlag, Berlin, 1989. Zbl0684.54001MR1039321
  6. Hoshina T., Yamazaki K., Weak C -embedding and P -embedding, and product spaces, Topology Appl. 125 (2002), 233-247. (2002) Zbl1013.54006MR1933574
  7. Yamazaki K., Absolute weak C -embedding in Hausdorff spaces, Topology Appl. 131 (2003), 273-279. (2003) Zbl1025.54010MR1983083

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