Revista Integración
ISSN 0120-419X ISSN 2145-8472
CASTILLO, Adriana C. HERNANDEZ A., Julio C.. The dual of the reflection of a topological group. []. , 39, 1, pp.23-40. 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.
: Dual groups; topological groups; reflections.