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Proceedings of the American Mathematical Society

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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
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.

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Keywords: Hyadic, $ {G_\kappa }$, semilattice, separable, cardinality, $ \pi $-weight
Article copyright: © Copyright 1988 American Mathematical Society