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Regularity of Richardson's Compactification

Published online by Cambridge University Press:  20 November 2018

R. J. Gazik
R. J. Gazik*
Affiliation:
Arkansas State University, State University, Arkansas
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In [7] Richardson constructed a Stone-Čech type compactification R(E) of a Hausdorff convergence space E. Two questions arise in this regard. First, when is R(E) homeomorphic to β(E), β(E) the topological Stone-Čech compactification of E, for a Tychonoff topological space E? Second, if E is a regular convergence space, when is R(E) regular? The last question is motivated by the study of regular compactifications in [6]. In section 2 it will be shown that a necessary and sufficient condition in answer to both questions, is that α = cl(α) for each nonconvergent ultrafilter α on E.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 26 , Issue 6 , December 1974 , pp. 1289 - 1293
Copyright
Copyright © Canadian Mathematical Society 1974

References

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