A further characteristic of abstract convexity structures on topological spaces

Abstract: In this paper, we give a characteristic of abstract convexity structures on topological spaces with selection property. We show that if a convexity structure defined on a topological space has the weak selection property then satisfies -condition. Moreover, in a compact convex subset of a topological space with convexity structure, the weak selection property implies the fixed point property. [Copyright &y& Elsevier]