A note on spaces with countable extent

Yan-Kui Song

Commentationes Mathematicae Universitatis Carolinae (2017)

  • Volume: 58, Issue: 3, page 397-399
  • ISSN: 0010-2628

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 ⊆ X with property P such that X = S t ( A , 𝒰 ) . In this note, we construct a Tychonoff pseudocompact SCE-space which is not star Lindelöf, which gives a negative answer to a question of Rojas-Sánchez and Tamariz-Mascarúa.

How to cite

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Song, Yan-Kui. "A note on spaces with countable extent." Commentationes Mathematicae Universitatis Carolinae 58.3 (2017): 397-399. <http://eudml.org/doc/294097>.

@article{Song2017,
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 $X=St(A,\mathcal \{U\})$. In this note, we construct a Tychonoff pseudocompact SCE-space which is not star Lindelöf, which gives a negative answer to a question of Rojas-Sánchez and Tamariz-Mascarúa.},
author = {Song, Yan-Kui},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {star properties; star Lindelöf; space with star countable extent},
language = {eng},
number = {3},
pages = {397-399},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {A note on spaces with countable extent},
url = {http://eudml.org/doc/294097},
volume = {58},
year = {2017},
}

TY - JOUR
AU - Song, Yan-Kui
TI - A note on spaces with countable extent
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2017
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 58
IS - 3
SP - 397
EP - 399
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 $X=St(A,\mathcal {U})$. In this note, we construct a Tychonoff pseudocompact SCE-space which is not star Lindelöf, which gives a negative answer to a question of Rojas-Sánchez and Tamariz-Mascarúa.
LA - eng
KW - star properties; star Lindelöf; space with star countable extent
UR - http://eudml.org/doc/294097
ER -

References

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  9. Rojas-Sánchez A.D., Tamariz-Mascarúa Á., Spaces with star countable extent, Comment. Math. Univ. Carolin. 57 (2016), no 3, 381–395. MR3554518

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