Countably compact, locally countable spaces
Author:
J. E. Vaughan
Journal:
Proc. Amer. Math. Soc. 80 (1980), 147153
MSC:
Primary 54D20; Secondary 54A25, 54D25, 54D30, 54G20
MathSciNet review:
574525
Fulltext PDF Free Access
Abstract 
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Abstract: The results of this paper provide a simple method for constructing locally countable spaces (not ) in which every infinite closed set has cardinality . The spaces are used in a variety of ways as counterexamples. One of these spaces may be considered as a countably compact version of the Katětov Hclosed extension of the natural numbers.
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 J. Ginsburg and V. Saks, Some applications of ultrafilters in topology, Pacific J. Math. 57 (1975), 403418. MR 0380736 (52:1633)
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 A. Hajnal and I. Juhász, Some remarks on a property of topological cardinal functions, Acta Math. Acad. Sci. Hungar. 24 (1973), 307312.
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 R. E. Hodel, The number of closed subsets of a topological space, Canad. J. Math. 30 (1978), 301314. MR 0464131 (57:4066)
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 I. Juhász, Cardinal functions in topology, Math. Centre Tracts, No. 34, Math. Centrum, Amsterdam, 1971. MR 0340021 (49:4778)
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 , Discrete sequences of points, Topology Proc. 3 (1978), 237265. MR 540494 (80k:54046)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S0002993919800574525X
PII:
S 00029939(1980)0574525X
Keywords:
Countably compact,
locally countable,
Hclosed,
property wD,
Katětov extension,
right separated,
Dcompact,
no nontrivial convergent sequences,
Baire space
Article copyright:
© Copyright 1980
American Mathematical Society
