Topologies on abelian groups and a topological five-lemma

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.

arXiv comment19 pages. Hypotheses on Lemma 2.13 and, consequently, Proposition 3.22 are fixed (now they are more restrictive)