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Proceedings of the American Mathematical Society

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On the density character of closed subgroups

Authors: John Ginsburg, M. Rajagopalan and Victor Saks
Journal: Proc. Amer. Math. Soc. 57 (1976), 148-150
MSC: Primary 22A05; Secondary 54A25
MathSciNet review: 0404513
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Abstract: Answering a question posed by W. W. Comfort, G. L. Itzkowitz, and K. A. Ross, it is shown that for every infinite cardinal number $ \alpha $ there are a Hausdorff topological group $ G$ and a closed subgroup $ H$ of $ G$ such that $ d(H) > d(G) = \alpha $ (here $ d$ denotes ``density character"). Specifically, for $ G$ we take the (appropriately topologized) free Abelian group $ A(\beta D)$ generated by the Stone-Čech compactification of the discrete space $ D$ with $ \vert D\vert = \alpha $.

References [Enhancements On Off] (What's this?)

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Keywords: Topological group, free topological group, density character, closed subgroup
Article copyright: © Copyright 1976 American Mathematical Society