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$ G\sb \kappa$ subspaces of hyadic spaces


Author: Murray G. Bell
Journal: Proc. Amer. Math. Soc. 104 (1988), 635-640
MSC: Primary 54D30; Secondary 54A25, 54B20
DOI: https://doi.org/10.1090/S0002-9939-1988-0962841-6
MathSciNet review: 962841
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Abstract: A hyadic space is a continuous image of a hyperspace of a compact space. For an infinite cardinal $ \kappa $, an intersection of at most $ \kappa $ many open subsets of $ X$ is called a $ {G_\kappa }$ subset of $ X$. We construct, in ZFC, a compact separable space of uncountable $ \pi $-weight and of cardinality continuum. This space is a $ {G_\omega }$ subset of a hyadic space. We show that a compact space that does not contain any convergent sequences and which contains the Stone-Čech compactification of the countable discrete space cannot be imbedded as a $ {G_\kappa }$ subset, where $ \kappa $ is less than the continuum, of any hyadic space.


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

  • [1] M. Bell, Generalized dyadic spaces, Fund. Math. 125 (1985), 47-58. MR 813988 (87d:54048)
  • [2] M. Bell and J. Pelant, Continuous images of compact semilattices, Canad. Math. Bull. 30 (1987), 109-113. MR 879879 (88c:54011)
  • [3] E. van Douwen, Mappings from hyperspaces and convergent sequences, manuscript.
  • [4] B. A. Efimov, Extremally disconnected compact spaces and absolutes, Trans. Moscow Math. Soc. 23 (1970), 243-285. MR 0418016 (54:6060)
  • [5] K. Hofmann, M. Mislove and A. Stralka, The Pontryagin duality of compact 0-dimensional semilattices and its applications, Lecture Notes in Math., Vol. 396, Springer-Verlag, Berlin, Heidelberg, and New York, 1974. MR 0354921 (50:7398)
  • [6] J. van Mill, Supercompactness and Wallman spaces, Math. Centre Tracts, Vol. 85, Mathematisch Centrum, Amsterdam 1977. MR 0464160 (57:4095)
  • [7] B. D. Sapirovskii, Maps onto Tikhonov cubes, Russian Math. Surveys 35 (1980), 145-156.

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1988-0962841-6
Keywords: Hyadic, $ {G_\kappa }$, semilattice, separable, cardinality, $ \pi $-weight
Article copyright: © Copyright 1988 American Mathematical Society

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