On Mackey topologies in topological abelian groups

Michael Barr and Heinrich Kleisli

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 $\cal C$.

Keywords: Mackey topologies, duality, topological abelian groups.

2000 MSC: 22D35, 22A05, 18A40.

Theory and Applications of Categories, Vol. 8, 2001, No. 4, pp 54-62.

http://www.tac.mta.ca/tac/volumes/8/n4/n4.dvi
http://www.tac.mta.ca/tac/volumes/8/n4/n4.ps
http://www.tac.mta.ca/tac/volumes/8/n4/n4.pdf
ftp://ftp.tac.mta.ca/pub/tac/html/volumes/8/n4/n4.dvi
ftp://ftp.tac.mta.ca/pub/tac/html/volumes/8/n4/n4.ps

Revised 2011-12-23. Original version at
http://www.tac.mta.ca/tac/volumes/8/n4/n4a.dvi
TAC Home