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Regular Quotients of Metric Spaces

Published online by Cambridge University Press:  20 November 2018

Brian Warrack
Brian Warrack*
Affiliation:
University of Alberta EdmontonCanada
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In this note we consider the class of topological spaces whose every Hausdorff quotient is regular (or equivalently, normal). Sufficient conditions in order that a space belongs to this class have appeared in papers by Morita [3], and more recently by MacDonald and Willard [2]. In both cases, the authors impose conditions implying paracompactness. We shall derive additional sufficient conditions here which show that paracompactness is not necessary in general.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 18 , Issue 4 , October 1975 , pp. 611 - 613
Copyright
Copyright © Canadian Mathematical Society 1975

References

1. Franklin, S. P., Spaces in which sequences suffice, Fund. Math. 57 (1965), 107–115.Google Scholar
2. MacDonald, S. and Willard, S., Domains of paracompactness and regularity, Canad. J. Math. 24 (1972), 1079–1085.Google Scholar
3. Morita, K., On decomposition spaces of locally compact spaces, Proc. Japan Acad. 32 (1956), 544–548.Google Scholar