Compact convex sets free of inner points in infinite-dimensional topological vector spaces

Abstract

An inner point of a non-singleton convex set M is a point (Formula presented.) satisfying that for all (Formula presented.) there exists (Formula presented.) such that (Formula presented.). We prove the existence of convex compact subsets free of inner points in the infinite-dimensional setting. Following our pathway to this result, we come up with other several geometric hits, such as the existence of a non-convex subset that coincides with its starlike envelope