Equicontinuity of Arcs in the Pointwise Dual of a Topological Abelian Group: In Honour of Manuel López-Pellicer

We introduce, for any topological abelian group G, the property of equicontinuity of arcs of \(G^\wedge _p\), the dual group of G endowed with its pointwise topology. We analyze the implications of this property, which we denote by EAP\(_\sigma \), and we present some representative examples. Furthermore we prove that if G satisfies EAP\(_\sigma \), every element of the arcwise connected component of \(G^\wedge _p\) can be written as \(\phi (1)\) for a suitable one-parameter subgroup \(\phi :\mathbb {R} \rightarrow G^\wedge _p\).