Continuous isomorphisms onto separable groups

Luis Felipe Morales López

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 Ic 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| 2c admits a separable, precompact, Hausdorff group topology, where c = 2!.

Keywords

Condensation; Continuous isomorphism; Separable groups; Subtopology

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Universitat Politècnica de València

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