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Topological Extension Properties and Projective Covers

Published online by Cambridge University Press:  20 November 2018

Haruto Ohta
Haruto Ohta*
Affiliation:
Shizuoka University, Ohya, Shizuoka, Japan
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Introduction. All spaces considered in this paper are assumed to be (Hausdorff) completely regular, and all maps are continuous. Let be a topological property of spaces. We shall identify with the class of spaces having . A space having is called a -space, and a subspace of a -space is called a -regular space. The class of -regular spaces is denoted by R(). Following [37], we call a closed hereditary, productive, topological property such that each -regular space has a -regular compactification a topological extension property, or simply, an extension property. In this paper, we restrict our attention to extension properties satisfying the following axioms:

(A1) The two-point discrete space has .

(A2) If each -regular space of nonmeasurable cardinal has , then = R().

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 34 , Issue 6 , 01 December 1982 , pp. 1255 - 1275
Copyright
Copyright © Canadian Mathematical Society 1982

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