Martín Peinador, ElenaChasco, M.J.2023-06-202023-06-201998-090035-759610.1216/rmjm/1181071826https://hdl.handle.net/20.500.14352/57592A theorem of Glicksberg states that, for an abelian group G, two locally compact topologies with the same set of continuous characters must coincide. In [12] it is asserted that this fact also holds for two Pontryagin reflexive topologies. We prove here that this statement is not correct, and we give some additional conditions under which it is true. We provide some examples of classes of groups determined by their continuous characters.engjournal articlehttp://projecteuclid.org/euclid.rmjm/1181071826open access515.1Continuous characterreflexive spacecompact-open topologyPontryagin dualityGlicksberg theoremMontel spaceTopología1210 Topología