Geodesic
Compactness and countable compactness in weak topologies
Studia Mathematica, Tome 112 (1994) no. 3, pp. 243-250

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

A bounded closed convex set K in a Banach space X is said to have quasi-normal structure if each bounded closed convex subset H of K for which diam(H) > 0 contains a point u for which ∥u-x∥ diam(H) for each x ∈ H. It is shown that if the convex sets on the unit sphere in X satisfy this condition (which is much weaker than the assumption that convex sets on the unit sphere are separable), then relative to various weak topologies, the unit ball in X is compact whenever it is countably compact.
DOI : 10.4064/sm-112-3-243-250
Keywords: weak topologies, compactness, countable compactness, quasi-normal structure, convexity structures

W. A. Kirk 1

1 
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W. A. Kirk. Compactness and countable compactness in weak topologies. Studia Mathematica, Tome 112 (1994) no. 3, pp. 243-250. doi: 10.4064/sm-112-3-243-250

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