On the extent of star countable spaces

Ofelia Alas; Lucia Junqueira; Jan Mill; Vladimir Tkachuk; Richard Wilson

Open Mathematics (2011)

  • Volume: 9, Issue: 3, page 603-615
  • ISSN: 2391-5455

Abstract

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For a topological property P, we say that a space X is star Pif for every open cover Uof the space X there exists Y ⊂ X such that St(Y,U) = X and Y has P. We consider star countable and star Lindelöf spaces establishing, among other things, that there exists first countable pseudocompact spaces which are not star Lindelöf. We also describe some classes of spaces in which star countability is equivalent to countable extent and show that a star countable space with a dense σ-compact subspace can have arbitrary extent. It is proved that for any ω 1-monolithic compact space X, if C p(X)is star countable then it is Lindelöf.

How to cite

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Ofelia Alas, et al. "On the extent of star countable spaces." Open Mathematics 9.3 (2011): 603-615. <http://eudml.org/doc/269470>.

@article{OfeliaAlas2011,
abstract = {For a topological property P, we say that a space X is star Pif for every open cover Uof the space X there exists Y ⊂ X such that St(Y,U) = X and Y has P. We consider star countable and star Lindelöf spaces establishing, among other things, that there exists first countable pseudocompact spaces which are not star Lindelöf. We also describe some classes of spaces in which star countability is equivalent to countable extent and show that a star countable space with a dense σ-compact subspace can have arbitrary extent. It is proved that for any ω 1-monolithic compact space X, if C p(X)is star countable then it is Lindelöf.},
author = {Ofelia Alas, Lucia Junqueira, Jan Mill, Vladimir Tkachuk, Richard Wilson},
journal = {Open Mathematics},
keywords = {Lindelöf property; Extent; Star properties; Star countable spaces; Star Lindelöf spaces; Pseudocompact spaces; Countably compact spaces; Function spaces; κ-monolithic spaces; Products of ordinals; P-spaces; Metalindelöf spaces; Discrete subspaces; Open expansions; extent; star properties; star countable spaces; star Lindelöf spaces; pseudocompact spaces; countably compact spaces; function spaces; -monolithic spaces; products of ordinals; -spaces; metalindelöf spaces; discrete subspaces; open expansions},
language = {eng},
number = {3},
pages = {603-615},
title = {On the extent of star countable spaces},
url = {http://eudml.org/doc/269470},
volume = {9},
year = {2011},
}

TY - JOUR
AU - Ofelia Alas
AU - Lucia Junqueira
AU - Jan Mill
AU - Vladimir Tkachuk
AU - Richard Wilson
TI - On the extent of star countable spaces
JO - Open Mathematics
PY - 2011
VL - 9
IS - 3
SP - 603
EP - 615
AB - For a topological property P, we say that a space X is star Pif for every open cover Uof the space X there exists Y ⊂ X such that St(Y,U) = X and Y has P. We consider star countable and star Lindelöf spaces establishing, among other things, that there exists first countable pseudocompact spaces which are not star Lindelöf. We also describe some classes of spaces in which star countability is equivalent to countable extent and show that a star countable space with a dense σ-compact subspace can have arbitrary extent. It is proved that for any ω 1-monolithic compact space X, if C p(X)is star countable then it is Lindelöf.
LA - eng
KW - Lindelöf property; Extent; Star properties; Star countable spaces; Star Lindelöf spaces; Pseudocompact spaces; Countably compact spaces; Function spaces; κ-monolithic spaces; Products of ordinals; P-spaces; Metalindelöf spaces; Discrete subspaces; Open expansions; extent; star properties; star countable spaces; star Lindelöf spaces; pseudocompact spaces; countably compact spaces; function spaces; -monolithic spaces; products of ordinals; -spaces; metalindelöf spaces; discrete subspaces; open expansions
UR - http://eudml.org/doc/269470
ER -

References

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