Properties related to star countability and star finiteness

Two star properties recently studied by Song and a generalization of countable compactness called weak star finiteness by Song and previously, 1-cl-starcompactness by Matveev and Ikenaga, are studied. We show that two of these properties coincide with feeble Lindelöfness and feeble compactness respe...

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Bibliographic Details
Published in:Topology and its applications 2017-04, Vol.221, p.432-439
Main Authors: Alas, Ofelia T., Wilson, Richard G.
Format: Article
Language:English
Subjects:
1-cl-star-Lindelöf space
1-cl-starcompact space
Almost star countable
Feebly compact space
Star countable space
Star finite space
Weakly star countable
Weakly star finite
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Summary:Two star properties recently studied by Song and a generalization of countable compactness called weak star finiteness by Song and previously, 1-cl-starcompactness by Matveev and Ikenaga, are studied. We show that two of these properties coincide with feeble Lindelöfness and feeble compactness respectively in the class of spaces with a dense set of isolated points. Preservation of one of these properties under products by compact and sequentially compact spaces is also considered.
ISSN:0166-8641
1879-3207
DOI:10.1016/j.topol.2017.02.021