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Associated Regular Spaces

Published online by Cambridge University Press:  20 November 2018

J. Pelham Thomas
J. Pelham Thomas*
Affiliation:
Western Carolina University, Cullowhee, North Carolina
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Let be any topological space. In this paper, we show that there is a unique regular topology on X which is coarser than such that if Y is any regular space, the continuous maps are the same for and . We shall call the regular topology associated with and the regular space associated with .

Information

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 20 , 1968 , pp. 1087 - 1092
Copyright
Copyright © Canadian Mathematical Society 1968

References

1. Norris, M.J., A Note on regular and completely regular topological spaces, Proc. Amer. Math. Soc. 1 (1950), 754–755.Google Scholar
2. Bourbaki, N., Eléments de mathématique, Livre III, Chapitre I, 3ème éd. (Hermann, Paris, 1961).Google Scholar