On a Semigroup Problem II

Abstract

We consider the following semigroup problem: is the closure of a semigroup S in a topological vector space X a group when S does not lie on “one side” of any closed hyperplane of X? Whereas for finite dimensional spaces, the answer is positive, we give a new example of infinite dimensional spaces where the answer is negative.

Keywords

• semigroup
• group
• linear topological space
• separation by functionals