On star covering properties related to countable compactness and pseudocompactness

Marcelo D. Passos; Heides L. Santana; Samuel G. da Silva

Commentationes Mathematicae Universitatis Carolinae (2017)

  • Volume: 58, Issue: 3, page 371-382
  • ISSN: 0010-2628

Abstract

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We prove a number of results on star covering properties which may be regarded as either generalizations or specializations of topological properties related to the ones mentioned in the title of the paper. For instance, we give a new, entirely combinatorial proof of the fact that Ψ -spaces constructed from infinite almost disjoint families are not star-compact. By going a little further we conclude that if X is a star-compact space within a certain class, then X is neither first countable nor separable. We also show that if a topological space is pseudonormal and has countable extent, then its Alexandroff duplicate satisfies property ( a ) . A number of problems and questions are also presented.

How to cite

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Passos, Marcelo D., Santana, Heides L., and Silva, Samuel G. da. "On star covering properties related to countable compactness and pseudocompactness." Commentationes Mathematicae Universitatis Carolinae 58.3 (2017): 371-382. <http://eudml.org/doc/294116>.

@article{Passos2017,
abstract = {We prove a number of results on star covering properties which may be regarded as either generalizations or specializations of topological properties related to the ones mentioned in the title of the paper. For instance, we give a new, entirely combinatorial proof of the fact that $\Psi $-spaces constructed from infinite almost disjoint families are not star-compact. By going a little further we conclude that if $X$ is a star-compact space within a certain class, then $X$ is neither first countable nor separable. We also show that if a topological space is pseudonormal and has countable extent, then its Alexandroff duplicate satisfies property $(a)$. A number of problems and questions are also presented.},
author = {Passos, Marcelo D., Santana, Heides L., Silva, Samuel G. da},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {star-compact spaces; spaces star determined by a finite number of convergent sequences; $(a)$-spaces; selectively $(a)$-spaces},
language = {eng},
number = {3},
pages = {371-382},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On star covering properties related to countable compactness and pseudocompactness},
url = {http://eudml.org/doc/294116},
volume = {58},
year = {2017},
}

TY - JOUR
AU - Passos, Marcelo D.
AU - Santana, Heides L.
AU - Silva, Samuel G. da
TI - On star covering properties related to countable compactness and pseudocompactness
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2017
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 58
IS - 3
SP - 371
EP - 382
AB - We prove a number of results on star covering properties which may be regarded as either generalizations or specializations of topological properties related to the ones mentioned in the title of the paper. For instance, we give a new, entirely combinatorial proof of the fact that $\Psi $-spaces constructed from infinite almost disjoint families are not star-compact. By going a little further we conclude that if $X$ is a star-compact space within a certain class, then $X$ is neither first countable nor separable. We also show that if a topological space is pseudonormal and has countable extent, then its Alexandroff duplicate satisfies property $(a)$. A number of problems and questions are also presented.
LA - eng
KW - star-compact spaces; spaces star determined by a finite number of convergent sequences; $(a)$-spaces; selectively $(a)$-spaces
UR - http://eudml.org/doc/294116
ER -

References

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