Non-Linear Inner Structure of Topological Vector Spaces

Inner structure appeared in the literature of topological vector spaces as a tool to characterize extremal convex sets. For instance, recent years, inner has been used provide solution The Faceless Problem and finest locally topology on real space. This manuscript goes one step further by settling bases for studying non-convex In first place, we observe that well behaviour sets with respect does not transport following sense: it already proved if face set intersects points, then is whole set; however, setting, find an example proper subset points. On opposite, prove non-necessarily affine internal coincides set. other hand, was isomorphisms translations preserve points outer this manuscript, show general, maps do Finally, making use structure, simple proof fact absorbing neighborhood 0 topology. fact, its which also interior