On the density character of closed subgroups-Reference-Cited by-同舟云学术

On the density character of closed subgroups

Published:1976 Issue:1 Volume:57 Page:148-150
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Ginsburg John,Rajagopalan M.,Saks Victor

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 α \alpha there are a Hausdorff topological group G G and a closed subgroup H H of G G such that d ( H ) > d ( G ) = α d(H) > d(G) = \alpha (here d d denotes “density character"). Specifically, for G G we take the (appropriately topologized) free Abelian group A ( β D ) A(\beta D) generated by the Stone-Čech compactification of the discrete space D D with | D | = α |D| = \alpha .

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/1976-057-01/S0002-9939-1976-0404513-4/S0002-9939-1976-0404513-4.pdf

Reference7 articles.

1. W. W. Comfort, Gerald L. Itzkowitz and Kenneth A. Ross, Density character in topological groups (to appear).

2. Die Grundlehren der mathematischen Wissenschaften, Band 211;Comfort, W. W.,1974

3. Free topological groups;Graev, M. I.;Izvestiya Akad. Nauk SSSR. Ser. Mat.,1948

4. The University Series in Higher Mathematics;Gillman, Leonard,1960

5. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences];Hewitt, Edwin,1979

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