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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| Format: | Article |
| Langue: | English |
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Universitat Politècnica de València
2012-10-01
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| Collection: | Applied General Topology |
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| Accès en ligne: | http://polipapers.upv.es/index.php/AGT/article/view/1625 |
| Résumé: | 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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| ISSN: | 1576-9402 1989-4147 |