Locally compact subgroups of metrizable topological abelian groups

Hooper, R. C.

doi:10.1090/S0002-9939-1976-0409710-X

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Locally compact subgroups of metrizable topological abelian groups
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Proc. Amer. Math. Soc. 57 (1976), 159-164 Request permission

Abstract:

This paper examines the question of existence of locally compact subgroups of topological abelian groups. A counterexample is given and it is shown in a certain setting that groups have a nontrivial locally compact subgroup.

References

S. Rolewicz, Some remarks on monothetic groups, Colloq. Math. 13 (1964), 27–28. MR 171876, DOI 10.4064/cm-13-1-27-28
Ivan Singer, Bases in Banach spaces. I, Die Grundlehren der mathematischen Wissenschaften, Band 154, Springer-Verlag, New York-Berlin, 1970. MR 0298399