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Special points in compact spaces


Author: Murray Bell
Journal: Proc. Amer. Math. Soc. 122 (1994), 619-624
MSC: Primary 54D30; Secondary 54C50, 54F65, 54G20
DOI: https://doi.org/10.1090/S0002-9939-1994-1246515-5
MathSciNet review: 1246515
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Abstract: Given a collection $ \mathcal{C}$, of cardinality $ \kappa$, of subsets of a compact space X, we prove the existence of a point x such that whenever $ C \in \mathcal{C}$ and $ X \in \bar C$, there exists a $ {G_\lambda }$-set Z with $ \lambda < \kappa $ and $ x \in Z \subset \bar C$. We investigate the case when $ \mathcal{C}$ is the collection of all cozerosets of X and also when X is a dyadic space. We apply this result to homogeneous compact spaces. Another application is a characterization of $ {2^{{\omega _1}}}$ among dyadic spaces.


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

  • [Be1] M. Bell, Nonhomogeneity of powers of Cor images, Rocky Mountain J. Math. 22 (1992), 805-812. MR 1183687 (93j:54014)
  • [Be2] -, Generalized dyadic spaces, Fund. Math. 125 (1985), 47-58. MR 813988 (87d:54048)
  • [Ef] B. Efimov, Dyadic bicompacta, Trans. Moscow Math. Soc. 14 (1965), 229-267. MR 0202105 (34:1979)
  • [En1] R. Engelking, Cartesian products and dyadic spaces, Fund. Math. 57 (1965), 287-303. MR 0196692 (33:4879)
  • [En2] -, General topology, Sigma Ser. Pure Math., vol. 6, Heldermann Verlag, Berlin, 1989.
  • [Ku] K. Kunen, Set theory, Stud. Logic Found. Math., vol. 120, North-Holland, Amsterdam, 1980.
  • [Mo] D. Motorov, Zero-dimensional and linearly ordered bicompacta, Russian Math. Surveys 44 (1989), 190-191. MR 1037015 (91c:54050)
  • [Pa] V. V. Pashenkov, Extensions of compact spaces, Soviet Math. Dokl. 15 (1974), 43-47.
  • [Sc] E. Schepin, Functors and uncountable powers of compacta, Russian Math. Surveys 36 (1981), 1-71. MR 622720 (82k:54012)
  • [Sh] L. Shapiro, On homogeneities of dyadic bicompacta, manuscript, 1993.

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1994-1246515-5
Keywords: Compact, cozeroset, dyadic, homogeneous, point
Article copyright: © Copyright 1994 American Mathematical Society

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