Hostname: page-component-586b7cd67f-dlnhk Total loading time: 0 Render date: 2024-11-26T13:42:45.043Z Has data issue: false hasContentIssue false
  • English
  • Français

On cardinal numbers associated with locally compact Abelian groups

Published online by Cambridge University Press:  24 October 2008

J. B. Reade
J. B. Reade
Affiliation:
Trinity College, Cambridge
Get access Rights & Permissions [Opens in a new window]

Extract

We are concerned in this work with the following question:

Suppose that i is a continuous algebraic isomorphism from the topological group H onto a subgroup of the topological group G and suppose that the image i(H) is not closed in G; then what can we say about the cardinal number

We observe two easy results.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 61 , Issue 1 , January 1965 , pp. 75 - 79
Copyright
Copyright © Cambridge Philosophical Society 1965

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Bourbaki, N.Topologie générale (Hermann; Paris, 1961).Google Scholar
(2)Kakutani, S.On cardinal numbers related with a compact Abelian group. Proc. Imp. Acad. Tokyo 19 (1943), 366–372.Google Scholar
(3)Kamke, E.Theory of sets (Dover; New York, 1950).Google Scholar
(4)Montgomery, D. and Zippin, L.Topological transformation groups (Interscience; New York, 1955).Google Scholar
(5)Varopoulos, N. Th.Studies in harmonic analysis. Proc. Cambridge Philos. Soc. 60 (1964), 465–516.CrossRefGoogle Scholar
(6)Varopoulos, N. Th.A theorem on cardinal numbers associated with a locally compact Abelian group. Proc. Cambridge Philos. Soc. 60 (1964), 701–704.CrossRefGoogle Scholar