# 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

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topOfelia 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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