Topologies on abelian groups and a topological five-lemma

2025/02/27 by Rivera-Mesas, Felipe · 1 citation
#22B05 #FOS: Mathematics #General Topology (math.GN) #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2502.20559

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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• Lichtenbaum-van Hamel duality for singular varieties over p-adic fields

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