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Spread and local properties


Author: Basil Coutant
Journal: Proc. Amer. Math. Soc. 112 (1991), 893-898
MSC: Primary 54A25; Secondary 03E50
DOI: https://doi.org/10.1090/S0002-9939-1991-1045132-7
MathSciNet review: 1045132
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Abstract: A technique for combining the spread of a space and several local properties is exploited to obtain decompositions of a space and cardinal function bounds on the size and weight. It is shown that a locally countable set is the union of $ {\omega _1}$ discrete sets and that under $ MA\left( {{\omega _1}} \right)$ the weight of a manifold is equal to its spread.


References [Enhancements On Off] (What's this?)

  • [1] U. Abraham and S. Todorčević, Martin's axiom and first-countable $ S$- and $ L$-spaces, Handbook of Set Theoretic Topology, North-Holland, Amsterdam, 1984, pp. 327-346.
  • [2] Z. Balogh, Locally nice spaces under Martin's axiom, Comment Math. Univ. Carolin. 24 (1983), 63-87. MR 703926 (85b:54005)
  • [3] B. Coutant, Some cardinal function relationships between $ {C_p}\left( X \right)$ and finite powers of a space $ X$, Topology Appl. (to appear). MR 1110568 (92j:54018)
  • [4] R. Engelking, General topology, Polish Scientific Publishers, Warsaw, 1977. MR 0500780 (58:18316b)
  • [5] D. Fremlin, Perfect pre-images of $ {\omega _1}$ and the PFA, Topology Appl. 29 (1988), 151-166. MR 949366 (89i:03096)
  • [6] R. Hodel, Cardinal functions I, Handbook of Set Theoretic Topology, North-Holland, Amsterdam, 1984, pp. 63-109. MR 776620 (86j:54007)
  • [7] I. Juhász, K. Kunen, and M. E. Rudin, Two more hereditarily separable non-Lindelöf spaces, Canad. J. Math. 28 (1976), 998-1005. MR 0428245 (55:1270)
  • [8] P. Nyikos, The theory of nonmetrizable manifolds, Handbook of Set Theoretic Topology, North-Holland, Amsterdam, 1984, pp. 633-684. MR 776633 (86f:54054)
  • [9] J. Roitman, Basic $ S$ and $ L$, Handbook of Set Theoretic Topology, North-Holland, Amsterdam, 1984, pp. 295-326. MR 776626 (87a:54043)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1991-1045132-7
Keywords: Cardinality of a space, locally countable, locally second countable, nonmetrizable manifolds, spread, $ S/L$-spaces, weight of a space
Article copyright: © Copyright 1991 American Mathematical Society

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