Topologies on abelian groups and a topological five-lemma
General Topology
2025-12-30 v3 Number Theory
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.
Cite
@article{arxiv.2502.20559,
title = {Topologies on abelian groups and a topological five-lemma},
author = {Felipe Rivera-Mesas},
journal= {arXiv preprint arXiv:2502.20559},
year = {2025}
}
Comments
19 pages. Hypotheses on Lemma 2.13 and, consequently, Proposition 3.22 are fixed (now they are more restrictive)