On endomorphisms of abelian topological groups

Authors:
Eli Katz and Sidney A. Morris

Journal:
Proc. Amer. Math. Soc. **85** (1982), 181-183

MSC:
Primary 22B05; Secondary 16A65

DOI:
https://doi.org/10.1090/S0002-9939-1982-0652437-2

MathSciNet review:
652437

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Abstract: A family of continuous endomorphisms of a topological group is said to be *small* if for every subgroup of of cardinality there exists an element such that . M. I. Kabenjuk [**5**] proved that if is a compact connected Hausdorff abelian group of countable weight then every countable family of nontrivial endomorphisms of is small. He asked if "compact" can be replaced by "complete". In this note the answer is given in the negative, but it is shown that "compact" can be replaced by "locally compact".

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1982-0652437-2

Keywords:
Endomorphism ring,
topological group,
abelian group,
representable ring

Article copyright:
© Copyright 1982
American Mathematical Society