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Proceedings of the American Mathematical Society

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A covering property which implies isocompactness. I


Authors: J. M. Worrell and H. H. Wicke
Journal: Proc. Amer. Math. Soc. 79 (1980), 331-334
MSC: Primary 54D20; Secondary 54D30
DOI: https://doi.org/10.1090/S0002-9939-1980-0565365-6
MathSciNet review: 565365
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Abstract: We define a covering property for a topological space which does not explicitly mention countability or finitude of collections although it generalizes weak $ \delta \theta $-refinability. We prove a general theorem that implies that countably compact spaces having the covering property are compact.


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DOI: https://doi.org/10.1090/S0002-9939-1980-0565365-6
Keywords: Countably compact, compact, closed-complete, weak $ \delta \theta $-refinability, closed ultrafilters, isocompactness, (weakly) $ {[\alpha ,\beta ]^r}$-refinable, (weakly) $ {[\alpha ,\infty )^r}$-refinable
Article copyright: © Copyright 1980 American Mathematical Society

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