subbases, convex sets, and hyperspaces - Semantic Scholar
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subbases, convex sets, and hyperspaces - Semantic Scholar
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PACIFIC JOURNAL OF MATHEMATICS Vol. 92, No. 2, 1981
SUBBASES, CONVEX SETS, AND HYPERSPACES JAN VAN MILL, MARCEL VAN DE VEL
We introduce a notion of topological convexity. Main topics are: compactness of convexity structures, continuity of convex closure operators, and characterization of convex sets. 1* Closed subbases* It will be assumed that all spaces are 2\. We agree to use the word "subbase" for "closed subbase". A subbase £f of a space X is called a Tx subbase if for each S e y and for each xeX - S there is an S' e 6^ with x e S' c X - S. £S is called a normal subbase if for each pair of sets Sl9 S2 e
