On Kuratowski’s problem in vector spaces

Abstract

It is a well known problem by Kuratowski that there are no more than 14 distinct sets by applying operations of the closure and complement, successively, on a subset A of a topological space X [1]. In this paper, we are interested to deal with the Kuratowski ’s problem in the setting of a vector space X by applying operations of the algebraic closure and algebraic interior for a convex subset A of X.