Extensions of Pseudometrics

Shapiro, H. L.

Canadian journal of mathematics, Tome 18 (1966) no. 1, pp. 981-998

Résumé

If γ is an infinite cardinal number, a subset S of a topological space X is said to be Pγ-embedded in X if every γ-separable continuous pseudometric on S can be extended to a γ-separable continuous pseudometric on X. (A pseudometric d on X is γ-separable if there exists a subset G of X such that |G| ⩽ 7 and such that G is dense in X relative to the pseudometric topology A pseudometric d is continuous if d is continuous relative to the product topology on X × X.) We say that S is P-embedded in X if every continuous pseudometric on S can be extended to a continuous pseudometric on X.

Détail

DOI : 10.4153/CJM-1966-099-0

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