Continuous isomorphisms onto separable groups

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...

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Main Author:	Luis Felipe Morales López
Format:	Article
Language:	English
Published:	Universitat Politècnica de València 2012-10-01
Series:	Applied General Topology
Subjects:	Condensation Continuous isomorphism Separable groups Subtopology
Online Access:	http://polipapers.upv.es/index.php/AGT/article/view/1625

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spelling	doaj-df50e01dba2c4ad1b8017e765bf5b6fc2020-11-24T23:52:59ZengUniversitat Politècnica de ValènciaApplied General Topology1576-94021989-41472012-10-0113213515010.4995/agt.2012.16251327Continuous isomorphisms onto separable groupsLuis Felipe Morales López0Universidad Autónoma Metropolitana - IztapalapaA 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!.http://polipapers.upv.es/index.php/AGT/article/view/1625CondensationContinuous isomorphismSeparable groupsSubtopology
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Luis Felipe Morales López
spellingShingle	Luis Felipe Morales López Continuous isomorphisms onto separable groups Applied General Topology Condensation Continuous isomorphism Separable groups Subtopology
author_facet	Luis Felipe Morales López
author_sort	Luis Felipe Morales López
title	Continuous isomorphisms onto separable groups
title_short	Continuous isomorphisms onto separable groups
title_full	Continuous isomorphisms onto separable groups
title_fullStr	Continuous isomorphisms onto separable groups
title_full_unstemmed	Continuous isomorphisms onto separable groups
title_sort	continuous isomorphisms onto separable groups
publisher	Universitat Politècnica de València
series	Applied General Topology
issn	1576-9402 1989-4147
publishDate	2012-10-01
description	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!.
topic	Condensation Continuous isomorphism Separable groups Subtopology
url	http://polipapers.upv.es/index.php/AGT/article/view/1625
work_keys_str_mv	AT luisfelipemoraleslopez continuousisomorphismsontoseparablegroups
_version_	1725471110322978816

Continuous isomorphisms onto separable groups

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