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Continuous isomorphisms onto separable groups
2013
Applied General Topology
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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.
doi:10.4995/agt.2012.1625
fatcat:w57xowrcvjfaxorxkywobmjs4q