Saddle point theorems on generalized convex spaces.
Semiconvex compacta
We define and investigate a generalization of the notion of convex compacta. Namely, for semiconvex combination in a semiconvex compactum we allow the existence of non-trivial loops connecting a point with itself. It is proved that any semiconvex compactum contains two non-empty convex compacta, the center and the weak center. The center is the largest compactum such that semiconvex combination induces a convex structure on it. The convex structure on the weak center does not necessarily coincide...
Simplicial homology of preconvexity spaces
Some characterization of infinite antimatroids.
Some extensions of the class of -convex bodies.
Starshapedness in convexity spaces
Strictly convex metric spaces with round balls and fixed points
The paper introduces a notion of strictly convex metric space and strictly convex metric space with round balls. These objects generalize the well known concept of strictly convex Banach space. We prove some fixed point theorems in strictly convex metric spaces with round balls.
Structures vectorielles et affines floues. Convexité
Superior estimation of Carathéodory's dimension for n-cell convexity
Sur les automorphismes affines des ouverts convexes saillants