Remarks on star covering properties in pseudocompact spaces

Mathematica Bohemica (2013)

• Volume: 138, Issue: 2, page 165-169
• ISSN: 0862-7959

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Abstract

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Let $P$ be a topological property. A space $X$ is said to be star $P$ if whenever $𝒰$ is an open cover of $X$, there exists a subspace $A\subseteq X$ with property $P$ such that $X=\mathrm{St}\left(A,𝒰\right)$, where $\mathrm{St}\left(A,𝒰\right)=\bigcup \left\{U\in 𝒰:U\cap A\ne \varnothing \right\}.$ In this paper, we study the relationships of star $P$ properties for $P\in \left\{\mathrm{Lindel}ö\mathrm{f},\mathrm{compact},\mathrm{countablycompact}\right\}$ in pseudocompact spaces by giving some examples.

How to cite

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Song, Yan-Kui. "Remarks on star covering properties in pseudocompact spaces." Mathematica Bohemica 138.2 (2013): 165-169. <http://eudml.org/doc/252530>.

@article{Song2013,
abstract = {Let $P$ be a topological property. A space $X$ is said to be star $P$ if whenever $\mathcal \{U\}$ is an open cover of $X$, there exists a subspace $A\subseteq X$ with property $P$ such that $X=\mathop \{\rm St\}(A,\mathcal \{U\})$, where $\mathop \{\rm St\}(A,\mathcal \{U\})=\bigcup \lbrace U\in \mathcal \{U\}\colon U\cap A\ne \emptyset \rbrace .$ In this paper, we study the relationships of star $P$ properties for $P\in \lbrace \textrm \{Lindelöf, compact, countably compact\}\rbrace$ in pseudocompact spaces by giving some examples.},
author = {Song, Yan-Kui},
journal = {Mathematica Bohemica},
keywords = {Lindelöf; star Lindelöf; compact; star compact; countably compact; star countably compact space; star covering property; start-Lindelöf; star compact; start countably compact},
language = {eng},
number = {2},
pages = {165-169},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Remarks on star covering properties in pseudocompact spaces},
url = {http://eudml.org/doc/252530},
volume = {138},
year = {2013},
}

TY - JOUR
AU - Song, Yan-Kui
TI - Remarks on star covering properties in pseudocompact spaces
JO - Mathematica Bohemica
PY - 2013
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 138
IS - 2
SP - 165
EP - 169
AB - Let $P$ be a topological property. A space $X$ is said to be star $P$ if whenever $\mathcal {U}$ is an open cover of $X$, there exists a subspace $A\subseteq X$ with property $P$ such that $X=\mathop {\rm St}(A,\mathcal {U})$, where $\mathop {\rm St}(A,\mathcal {U})=\bigcup \lbrace U\in \mathcal {U}\colon U\cap A\ne \emptyset \rbrace .$ In this paper, we study the relationships of star $P$ properties for $P\in \lbrace \textrm {Lindelöf, compact, countably compact}\rbrace$ in pseudocompact spaces by giving some examples.
LA - eng
KW - Lindelöf; star Lindelöf; compact; star compact; countably compact; star countably compact space; star covering property; start-Lindelöf; star compact; start countably compact
UR - http://eudml.org/doc/252530
ER -

References

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