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Spaces in which the nondegenerate connected sets are the cofinite sets


Author: Gary Gruenhage
Journal: Proc. Amer. Math. Soc. 122 (1994), 911-924
MSC: Primary 54D05; Secondary 54A35, 54G20
DOI: https://doi.org/10.1090/S0002-9939-1994-1287102-2
MathSciNet review: 1287102
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Abstract: Assuming the continuum hypothesis (CH), we construct a perfectly normal space X such that $ Y \subset X$ is connected and nondegenerate iff $ X\backslash Y$ is finite. We also show that completely regular, as well as countable Hausdorff, examples of this kind can be obtained under axioms weaker than CH, e.g., Martin's Axiom.


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  • [E] P. Erdös, Some remarks on connected sets, Bull. Amer. Math. Soc. 50 (1944), 442-446. MR 0010603 (6:43a)
  • [K] K. Kunen, Set theory, North-Holland, Amsterdam, 1990. MR 756630 (85e:03003)
  • [Ts] S. F. Tsvid, A countable strongly unicoherent space, Mat. Zemetki 24 (1978), 655-657. MR 509913 (80b:54045)
  • [Tz] V. Tzannes, Three countable connected spaces, Colloq. Math. 56 (1988), 267-279. MR 991215 (91a:54027)
  • [V] J. E. Vaughan, Small uncountable cardinals and topology, Open Problems in Topology (J. van Mill and G. M. Reed, eds.), North-Holland, Amsterdam, 1990. MR 1078636 (92c:54001)
  • [W] S.Watson, Problems I wish I could solve, Open Problems in Topology (J. van Mill and G. M. Reed, eds.), North-Holland, Amsterdam, 1990. MR 1078640

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DOI: https://doi.org/10.1090/S0002-9939-1994-1287102-2
Article copyright: © Copyright 1994 American Mathematical Society

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