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A theorem on cardinal numbers associated with inductive limits of locally compact Abelian groups

Published online by Cambridge University Press:  24 October 2008

J. B. Reade
J. B. Reade
Affiliation:
Trinity College, Cambridge
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Extract

Our motivation for this paper is to be found in (2) and (3). In (2) Varopoulos considers inductive limits of topological groups, in particular what he calls ‘ℒ∞’. (He calls a topology an ℒ∞-topology when it is the inductive limit of a decreasing sequence of locally compact Hausdorff topologies.) In (2) he proves that much of the classical theory of locally compact Abelian groups also goes through for Abelian ℒ∞-groups, in particular Pontrjagin duality.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 61 , Issue 1 , January 1965 , pp. 69 - 74
Copyright
Copyright © Cambridge Philosophical Society 1965

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References

REFERENCES

(1)Kakutani, S.On cardinal numbers related with a compact Abelian group. Proc. Imp. Acad. Tokyo 19 (1943), 366–372.Google Scholar
(2)Varopoulos, N. Th.Studies in harmonic analysis. Proc. Cambridge Philos. Soc. 60 (1964), 465–516.CrossRefGoogle Scholar
(3)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