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Perfect Maps and Epi-Reflective Hulls

Published online by Cambridge University Press:  20 November 2018

Anthony W. Hager
Anthony W. Hager*
Affiliation:
Wesleyan University, Middletown, Connecticut
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The main theorems concern the relation between the - compact spaces and the -regular spaces, and their analogues in uniform spaces. In either of the categories of Tychonoff spaces or uniform spaces, let be a class of spaces, let be the epi-reflective hull of se (closed subspaces of products of members of ), let be the “onto-reflective” hull of (all subspaces of products of members of ), and let r and o be the associated functors. Let be the class of spaces which admit a perfect map into a member of . Then, is epi-reflective (and in Tych, = but in Unif, the equality fails); call the functor p.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 27 , Issue 1 , 01 February 1975 , pp. 11 - 24
Copyright
Copyright © Canadian Mathematical Society 1975

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