Geodesic
On Mackey topologies in topological abelian groups
Theory and applications of categories, Tome 8 (2001), pp. 54-62

Voir la notice de l'article provenant de la source Theory and Applications of Categories website

Let $\cal C$ be a full subcategory of the category of topological abelian groups and SP$\cal C$ denote the full subcategory of subobjects of products of objects of $\cal C$. We say that SP$\cal C$ has Mackey coreflections if there is a functor that assigns to each object $A$ of SP$\cal C$ an object $\tau A$ that has the same group of characters as $A$ and is the finest topology with that property. We show that the existence of Mackey coreflections in SP$\cal C$ is equivalent to the injectivity of the circle with respect to topological subgroups of groups in $\cal C$.

Classification : 22D35, 22A05, 18A40.
Keywords: Mackey topologies, duality, topological abelian groups. 
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     author = {Michael Barr and Heinrich Kleisli},
     title = {On {Mackey} topologies in topological abelian groups},
     journal = {Theory and applications of categories},
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     volume = {8},
     year = {2001},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2001_8_a3/}
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Michael Barr; Heinrich Kleisli. On Mackey topologies in topological abelian groups. Theory and applications of categories, Tome 8 (2001), pp. 54-62. http://geodesic.mathdoc.fr/item/TAC_2001_8_a3/