Vector optimization in real linear spaces: The role of core convex topology

Majid Soleimani-damaneh, Ashkan Mohammadi [Wayne State University]

In this paper, the Core Convex Topology (CCT) on a real vector space $X$, as the strongest topology which makes $X$ into a locally convex space, is reconstructed. It is shown that the algebraic interior and the vectorial closure notions, considered in the literature as replacements of topological interior and closure, respectively, in linear spaces without topology, are actually nothing else than the interior and closure w.r.t. the CCT. After reconstructing the CCT and investigating it, we show that the properties of this topology lead to directly extending various important results in vector optimization from topological vector spaces to real vector spaces.