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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

1. Banaschewski, B., Extensions of topological spaces, Can. Math. Bull. 7 (1964), 1–22.Google Scholar
2. Biesterfeldt, H. J., Regular convergence spaces, Indag. Math. 28 (1966), 605–607.Google Scholar
3. Blaszczyk, A., On locally H-closed spaces and the Fomin H-closed extension, Colloq. Math. 25 (1972), 241–253.Google Scholar
4. Kent, D. C. and Richardson, G. D., Minimal convergence spaces, Trans. Amer. Math. Soc. 160 (1971), 487–499.Google Scholar
5. Noble, N., Products with closed projections, Trans. Amer. Math. Soc. 260 (1971), 169–183.Google Scholar
6. Richardson, G. D. and Kent, D. C., Regular compactifications of convergence spaces, Proc. Amer. Math. Soc. 81 (1972), 571–573.Google Scholar
7. Richardson, G. D., A Stone-Čech compactification for limit spaces, Proc. Amer. Math. Soc. 25 (1970), 403–404.Google Scholar