Spaces with star countable extent

A. D. Rojas-Sánchez; Angel Tamariz-Mascarúa

Commentationes Mathematicae Universitatis Carolinae (2016)

  • Volume: 57, Issue: 3, page 381-395
  • ISSN: 0010-2628

Abstract

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For a topological property P , we say that a space X is star P if for every open cover 𝒰 of the space X there exists A ⊂ X such that s t ( A , 𝒰 ) = X . We consider space with star countable extent establishing the relations between the star countable extent property and the properties star Lindelöf and feebly Lindelöf. We describe some classes of spaces in which the star countable extent property is equivalent to either the Lindelöf property or separability. An example is given of a Tychonoff star Lindelöf space with a point countable base which is not star countable.

How to cite

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Rojas-Sánchez, A. D., and Tamariz-Mascarúa, Angel. "Spaces with star countable extent." Commentationes Mathematicae Universitatis Carolinae 57.3 (2016): 381-395. <http://eudml.org/doc/286850>.

@article{Rojas2016,
abstract = {For a topological property $P$, we say that a space $X$ is star $P$ if for every open cover $\mathcal \{U\}$ of the space $X$ there exists $A\subset X$ such that $st (A,\mathcal \{U\})= X$. We consider space with star countable extent establishing the relations between the star countable extent property and the properties star Lindelöf and feebly Lindelöf. We describe some classes of spaces in which the star countable extent property is equivalent to either the Lindelöf property or separability. An example is given of a Tychonoff star Lindelöf space with a point countable base which is not star countable.},
author = {Rojas-Sánchez, A. D., Tamariz-Mascarúa, Angel},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {extent; star properties; star countable spaces; star Lindelöf spaces; feebly Lindelöf spaces},
language = {eng},
number = {3},
pages = {381-395},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Spaces with star countable extent},
url = {http://eudml.org/doc/286850},
volume = {57},
year = {2016},
}

TY - JOUR
AU - Rojas-Sánchez, A. D.
AU - Tamariz-Mascarúa, Angel
TI - Spaces with star countable extent
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2016
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 57
IS - 3
SP - 381
EP - 395
AB - For a topological property $P$, we say that a space $X$ is star $P$ if for every open cover $\mathcal {U}$ of the space $X$ there exists $A\subset X$ such that $st (A,\mathcal {U})= X$. We consider space with star countable extent establishing the relations between the star countable extent property and the properties star Lindelöf and feebly Lindelöf. We describe some classes of spaces in which the star countable extent property is equivalent to either the Lindelöf property or separability. An example is given of a Tychonoff star Lindelöf space with a point countable base which is not star countable.
LA - eng
KW - extent; star properties; star countable spaces; star Lindelöf spaces; feebly Lindelöf spaces
UR - http://eudml.org/doc/286850
ER -

References

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