On some classes of spaces with the D -property

Juan Carlos Martínez

Commentationes Mathematicae Universitatis Carolinae (2014)

  • Volume: 55, Issue: 2, page 247-256
  • ISSN: 0010-2628

Abstract

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We shall prove that under CH every regular meta-Lindelöf P -space which is locally D has the D -property. In addition, we shall prove that a regular submeta-Lindelöf P -space is D if it is locally D and has locally extent at most ω 1 . Moreover, these results can be extended from the class of locally D -spaces to the wider class of 𝔻 -scattered spaces. Also, we shall give a direct proof (without using topological games) of the result shown by Peng [On spaces which are D, linearly D and transitively D, Topology Appl. 157 (2010), 378–384] which states that every weak θ ¯ -refinable 𝔻 -scattered space is D .

How to cite

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Martínez, Juan Carlos. "On some classes of spaces with the $D$-property." Commentationes Mathematicae Universitatis Carolinae 55.2 (2014): 247-256. <http://eudml.org/doc/261869>.

@article{Martínez2014,
abstract = {We shall prove that under CH every regular meta-Lindelöf $P$-space which is locally $D$ has the $D$-property. In addition, we shall prove that a regular submeta-Lindelöf $P$-space is $D$ if it is locally $D$ and has locally extent at most $\omega _1$. Moreover, these results can be extended from the class of locally $D$-spaces to the wider class of $\mathbb \{D\}$-scattered spaces. Also, we shall give a direct proof (without using topological games) of the result shown by Peng [On spaces which are D, linearly D and transitively D, Topology Appl. 157 (2010), 378–384] which states that every weak $\overline\{\theta \}$-refinable $\mathbb \{D\}$-scattered space is $D$.},
author = {Martínez, Juan Carlos},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {property $D$; meta-Lindelöf; weak $\overline\{\theta \}$-refinable; $P$-space; scattered space; property ; meta-Lindelöf; weak -refinable; -space; scattered space},
language = {eng},
number = {2},
pages = {247-256},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On some classes of spaces with the $D$-property},
url = {http://eudml.org/doc/261869},
volume = {55},
year = {2014},
}

TY - JOUR
AU - Martínez, Juan Carlos
TI - On some classes of spaces with the $D$-property
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2014
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 55
IS - 2
SP - 247
EP - 256
AB - We shall prove that under CH every regular meta-Lindelöf $P$-space which is locally $D$ has the $D$-property. In addition, we shall prove that a regular submeta-Lindelöf $P$-space is $D$ if it is locally $D$ and has locally extent at most $\omega _1$. Moreover, these results can be extended from the class of locally $D$-spaces to the wider class of $\mathbb {D}$-scattered spaces. Also, we shall give a direct proof (without using topological games) of the result shown by Peng [On spaces which are D, linearly D and transitively D, Topology Appl. 157 (2010), 378–384] which states that every weak $\overline{\theta }$-refinable $\mathbb {D}$-scattered space is $D$.
LA - eng
KW - property $D$; meta-Lindelöf; weak $\overline{\theta }$-refinable; $P$-space; scattered space; property ; meta-Lindelöf; weak -refinable; -space; scattered space
UR - http://eudml.org/doc/261869
ER -

References

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