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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
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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  • [B] R. L. Blair, Closed-completeness in spaces with weak covering properties, Set-Theoretic Topology, Academic Press, New York, 1977, pp. 17-45. MR 0464153 (57:4088)
  • [E] R. Engelking, General topology, Polish Scientific Publishers, Warsaw, 1977. MR 0500780 (58:18316b)
  • [FL] P. Fletcher and W. F. Lindgren, $ \theta $-spaces, General Topology and Appl. 9 (1978), 139-153. MR 0500849 (58:18362)
  • [HV] R. E. Hodel and J. E. Vaughan, A note on $ [a,b]$-compactness, General Topology and Appl. 4 (1974), 179-189. MR 0341402 (49:6153)
  • [M] R. L. Moore, Foundations of point set theory, rev. ed., Amer. Math. Soc. Colloq. Publ., vol. 13, Amer. Math. Soc., Providence, R. I., 1962. MR 0150722 (27:709)
  • [WW$ _{1}$] H. H. Wicke and J. M. Worrell, Jr., The hereditary Lindelöf property, primitive structures, and separable metrizability, Notices Amer. Math. Soc. 22 (1975), A-425.
  • [WW$ _{2}$] H. H. Wicke and J. M. Worrell, Jr., Point-countability and compactness, Proc. Amer. Math. Soc. 55 (1976), 427-431. MR 0400166 (53:4001)
  • [WoW] J. M. Worrell, Jr. and H. H. Wicke, Characterizations of developable topological spaces, Canad. J. Math. 17 (1965), 820-830. MR 0182945 (32:427)

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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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