Topological Extension Properties and Projective Covers

Ohta, Haruto

Canadian journal of mathematics, Tome 34 (1982) no. 6, pp. 1255-1275

Résumé

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().

Détail

DOI : 10.4153/CJM-1982-088-4

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