Abstract

CASTILLO, Adriana C.  and  HERNANDEZ A., Julio C.. The dual of the reflection of a topological group. Integración - UIS [online]. 2021, vol.39, n.1, pp.23-40.  Epub Feb 28, 2021. ISSN 0120-419X.  https://doi.org/10.18273/revint.v39n1-2021002.

In this paper we present a study of the duality of a group via reflections. We begin with the demonstration of a necessary condition for the continuity of the dual homomorphism of the homomorphism that goes from the group to its reflection, that is, if φ: G → ξ(G), it follows that→ is a continuous bijection for T ∈ ξ, where ξ is a reflective subcategory of the category of topological groups and ξ(G) is the reflection of G. Once the previous condition is met, it is shown that, when G is either a compact group or a topological group ech complete with φ: G → ξ(G) surjective and open or a locally compact topological group and φ: G → ξ(G) is surjective and open.

In the case of the dual reflections of metrizable topological groups, we rely on a result of Chasco [5] which implies that when G is a metrizable abelian topological group and H is a dense subgroup of G, then the dual groups and are topologically isomorphic.

Keywords : Dual groups; topological groups; reflections.

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