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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On the density character of closed subgroups
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by John Ginsburg, M. Rajagopalan and Victor Saks PDF
Proc. Amer. Math. Soc. 57 (1976), 148-150 Request permission

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 $|D| = \alpha$.
References
    W. W. Comfort, Gerald L. Itzkowitz and Kenneth A. Ross, Density character in topological groups (to appear).
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Additional Information
  • © Copyright 1976 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 57 (1976), 148-150
  • MSC: Primary 22A05; Secondary 54A25
  • DOI: https://doi.org/10.1090/S0002-9939-1976-0404513-4
  • MathSciNet review: 0404513