The Tubby Torus as a Quotient Group

Abstract

Let E be any metrizable nuclear locally convex space and E ^ the Pontryagin dual group of E. Then the topological group E ^ has the tubby torus (that is, the countably infinite product of copies of the circle group) as a quotient group if and only if E does not have the weak topology. This extends results in the literature related to the Banach−Mazur separable quotient problem.

Keywords

• torus
• tubby torus
• separable quotient problem
• locally convex space
• nuclear space
• banach space
• pontryagin duality
• weak topology