Embedding into discretely absolutely star-Lindelöf spaces

Yan-Kui Song

Commentationes Mathematicae Universitatis Carolinae (2007)

  • Volume: 48, Issue: 2, page 303-309
  • ISSN: 0010-2628

Abstract

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A space X is discretely absolutely star-Lindelöf if for every open cover 𝒰 of X and every dense subset D of X , there exists a countable subset F of D such that F is discrete closed in X and St ( F , 𝒰 ) = X , where St ( F , 𝒰 ) = ⋃ { U ∈ 𝒰 : U ∩ F ≠ ∅ } . We show that every Hausdorff star-Lindelöf space can be represented in a Hausdorff discretely absolutely star-Lindelöf space as a closed subspace.

How to cite

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Song, Yan-Kui. "Embedding into discretely absolutely star-Lindelöf spaces." Commentationes Mathematicae Universitatis Carolinae 48.2 (2007): 303-309. <http://eudml.org/doc/250189>.

@article{Song2007,
abstract = {A space $X$ is discretely absolutely star-Lindelöf if for every open cover $\mathcal \{U\}$ of $X$ and every dense subset $D$ of $X$, there exists a countable subset $F$ of $D$ such that $F$ is discrete closed in $X$ and $\operatorname\{St\}(F,\mathcal \{U\})=X$, where $\operatorname\{St\}(F,\{\mathcal \{U\}\}) = \bigcup \lbrace U\in \{\mathcal \{U\}\} : U\cap F\ne \emptyset \rbrace $. We show that every Hausdorff star-Lindelöf space can be represented in a Hausdorff discretely absolutely star-Lindelöf space as a closed subspace.},
author = {Song, Yan-Kui},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {normal; star-Lindelöf; centered-Lindelöf; star-Lindelöf space; centered-Lindelöf space; linked-Lindelöf space; absolutely discretely star-Lindelöf space},
language = {eng},
number = {2},
pages = {303-309},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Embedding into discretely absolutely star-Lindelöf spaces},
url = {http://eudml.org/doc/250189},
volume = {48},
year = {2007},
}

TY - JOUR
AU - Song, Yan-Kui
TI - Embedding into discretely absolutely star-Lindelöf spaces
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2007
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 48
IS - 2
SP - 303
EP - 309
AB - A space $X$ is discretely absolutely star-Lindelöf if for every open cover $\mathcal {U}$ of $X$ and every dense subset $D$ of $X$, there exists a countable subset $F$ of $D$ such that $F$ is discrete closed in $X$ and $\operatorname{St}(F,\mathcal {U})=X$, where $\operatorname{St}(F,{\mathcal {U}}) = \bigcup \lbrace U\in {\mathcal {U}} : U\cap F\ne \emptyset \rbrace $. We show that every Hausdorff star-Lindelöf space can be represented in a Hausdorff discretely absolutely star-Lindelöf space as a closed subspace.
LA - eng
KW - normal; star-Lindelöf; centered-Lindelöf; star-Lindelöf space; centered-Lindelöf space; linked-Lindelöf space; absolutely discretely star-Lindelöf space
UR - http://eudml.org/doc/250189
ER -

References

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