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
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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