UMAP Classes of Groups

A class g of maximally almost periodic (MAP) topological Abelian groups is called a UMAP-class if it has the following property: if G is an Abelian group and τ 1 and τ 2 are distinct group topologies in G such that (G, τ 1) and (G, τ 2) are in g, then (G, τ 1)∧ ≠ (G, τ 2)∧. Several examples of UMAP-classes are discussed. In particular, it is shown that the class PMAP of all Polish MAP-groups is a UMAP-class. © 2014 Springer Science+Business Media New York.