Continuous isomorphisms onto separable groups

Luis Felipe Morales López

Mexico

Universidad Autónoma Metropolitana - Iztapalapa

Posgrado enMatemáticas, Departamento de Matemáticas, Universidad Autónoma Metropolitana - Iztapalapa, Av. San Rafael Atlixco 186, Col. Vicentina, Iztapalapa, C.P. 09340, D.F., México.

Submitted: 2013-07-26

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Accepted: 2013-07-26

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DOI: https://doi.org/10.4995/agt.2012.1625
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Keywords:

Condensation, Continuous isomorphism, Separable groups, Subtopology

Supporting agencies:

This research was not funded

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!.
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