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Proceedings of the American Mathematical Society

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

 

 

Can an $ {\rm LCA}$ group be anti-self-dual?


Author: D. L. Armacost
Journal: Proc. Amer. Math. Soc. 27 (1971), 186-188
MSC: Primary 22.20
DOI: https://doi.org/10.1090/S0002-9939-1971-0267036-7
MathSciNet review: 0267036
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Abstract: We say that a topological group $ G$ is anti-self-dual if there are no nontrivial continuous homomorphisms from $ G$ into the character group $ \hat G$ or from $ \hat G$ into $ G$. We show that no nontrivial LCA group can be anti-self-dual.


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DOI: https://doi.org/10.1090/S0002-9939-1971-0267036-7
Keywords: Continuous homomorphisms, character group, densely divisible, reduced, anti-self-dual, compact elements
Article copyright: © Copyright 1971 American Mathematical Society