... xÎ) Î I(x9, xx) Φ 0;. (iii) for each S e ^ and x, x' eS, I(x, xf) cS. Î .... boundary of the Hubert cube, [11, Thm. 3.4], and Van de Vel used it to prove the Lef schetz ...
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
