Topologies on abelian groups and a topological five-lemma

Felipe Rivera-Mesas

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arXiv · 2502.20559

Topologies on abelian groups and a topological five-lemma

Felipe Rivera-Mesas

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Abstract

In this article we establish some results that allow to deduce the continuity of homomorphisms of (topological) abelian groups from commutative diagrams. In particular, we present a new topological version of the classical Five-Lemma. These results aim to be applied in duality results between cohomology groups in arithmetical contexts. In such a topological-arithmetical context, Pontryagin duality plays a central role and it becomes necessary to know whether certain homomorphisms are continuous.

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Felipe Rivera-Mesas. 2025-02-27. Topologies on abelian groups and a topological five-lemma. https://arxiv.org/abs/2502.20559

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