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Separation axioms and subcategories of top

Published online by Cambridge University Press:  09 April 2009

Ryosuke Nakagawa
Ryosuke Nakagawa
Affiliation:
Department of Mathematics, University of Tsukuba Ibaraki, Japan.
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Abstract

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(Point, closed subset)-separation axioms and closed subsets separation axioms for topological spaces will be uniformly defined. Then it is shown that a subcategory of TOP is bireflective in TOP if and only if Ob consists of all separated spaces for some (point, closed subset)-separation axiom. A characterization theorem on subcategories of all separated spaces for closed subsets separation axioms is also given by using the category SEP of all separation spaces and the embedding functor G: TOP → SEP. As an application we have that a T1-space is normal if and only if it is embedded in a product space of the unit intervals in SEP.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 22 , Issue 4 , December 1976 , pp. 476 - 490
Copyright
Copyright © Australian Mathematical Society 1976

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