Closed Maps and Paracompact Spaces

Shapiro, H. L.

Canadian journal of mathematics, Tome 20 (1968) no. 1, pp. 513-519

Résumé

Let ƒ be a map from a topological space X into a topological space F. We say that ƒ is proper in case ƒ is closed continuous and ƒ-1(y) is compact for all y ∊ Y. Proper maps have been extensively studied, see for example (3, Chapter I, §10) or (6). (The definition of a proper map given above is different from, but equivalent to, that given by Bourbaki in (3). In (6) only surjective proper maps are considered and these maps are called ƒitting maps.) It is known that if ƒ is a proper map, then X is compact if and only if ƒ(X) is compact, and X is paracompact if and only if ƒ(X) is paracompact.

Détail

DOI : 10.4153/CJM-1968-053-2

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