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Character-pure locally compact abelian groups and their dual groups

Published online by Cambridge University Press:  24 October 2008

Yuji Takahashi
Yuji Takahashi
Affiliation:
Department of Mathematics, Kushiro Public University of Economics, Kushiro City, 085, Japan
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Abstract

We give some characterizations of the class of character-pure locally compact abelian groups. As an application we supplement a result of Venkataraman characterizing the class of locally compact abelian groups which are topologically pure in their Bohr compactifications. We also study the class of locally compact abelian groups which are pure closed in their Bohr compactifications.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 108 , Issue 2 , September 1990 , pp. 311 - 315
Copyright
Copyright © Cambridge Philosophical Society 1990

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References

REFERENCES

[1]Armacost, D. L.. The Structure of Locally Compact Abelian Groups (Marcel Dekker Inc., 1981).Google Scholar
[2]Hewitt, E. and Ross, K. A.. Abstract Harmonic Analysis, vol. 1, 2nd edition (Springer-Verlag, 1979).CrossRefGoogle Scholar
[3]Robertson, L. C.. Connectivity, divisibility, and torsion. Trans. Amer. Math. Soc. 128 (1967), 482–505.CrossRefGoogle Scholar
[4]Venkataraman, R.. On locally compact abelian groups which are topologically pure in their Bohr compactifications. Fund. Math. 69 (1970), 103–107.CrossRefGoogle Scholar