Martín Peinador, ElenaChasco, M. J.Amigó, J. M.Cánovas, M. J.López-Cerdá, M. A.López-Pellicer, M.2023-07-122023-07-122023-07-0210.1007/978-3-031-30014-1_5https://hdl.handle.net/20.500.14352/87220We define the β-duality for topological Abelian groups by means of the notion of Hejcman of boundedness in uniform spaces. A real locally convex space considered as an Abelian topological group is β-reflexive iff it is reflexive in the ordinary sense for locally convex spaces. Thus, β-reflexivity is the natural extension to Abelian topological groups of the well-known notion of reflexivity. We prove: 1) A locally compact Abelian group is β-reflexive. 2) A β-reflexive metrizable group is reflexive in Pontryagin sense. 3) The β-bidual of a metrizable group is also a metrizable group.engbook parthttps://link.springer.com/chapter/10.1007/978-3-031-30014-1_5#citeasopen access512H-bounded setReflexiveEquicontinuousPrecompactSchwartz groupLocally convex spaceÁlgebraÁlgebra1201 Álgebra