Dual properties in totally bounded Abelian groups (Q1401911)

Let \(T\) denote the category of totally bounded Abelian groups and their continuous homomorphisms. To each object \(G\) in \(T\) there is associated a dual group \(G'\), also in \(T\), such that \(G''\) is canonically isomorphic to \(G\). Two topological properties \((P,Q)\) are in duality if for each \(G\) in \(T\) the following holds: \(G\) satisfies \(P\) if and only if \(G'\) satisfies \(Q\). The authors find the dual properties of realcompactness, hereditary realcompactness and pseudocompactness. They also show that if \(G\) is a countably pseudocompact group then \(G'\) is a \(\mu\) space.