Continuous isomorphisms onto separable groups

Abstract

A condensation is a one-to-one continuous function onto. We give sufficient conditions for a Tychonoff space to admit a condensation onto a separable dense subspace of the Tychonoff cube I c and discuss the differences that arise when we deal with topological groups, where condensation is understood as a continuous isomorphism. We also show that every Abelian group G with |G| ≤ 2 c admits a separable, precompact, Hausdorff group topology, where c = 2 ω .2010 MSC: 22A05, 54H11.