Direct limit topologies in the categories of topological groups and of uniform spaces

Details Direct limit topologies in the categories of topological groups and of uniform spaces Direct limit topologies in the categories of topological groups and of uniform spaces

2009-11-20

arxiv.org/abs/0911.3985v2

Tohoku Math. J. 64:1 (2012), 1-24

Mathematics

General Topology

20 pages

Scientific paper

We study the topological structure of the direct limit $\glim G_n$ of a tower
of topological groups $(G_n)$ in the category of topological groups and show
that under some conditions on the tower $(G_n)$ the topology of $\glim G_n$
coincides with the topology of the direct limit $\ulim G_n$ of the groups $G_n$
endowed with the Roelcke uniformity in the category of uniform spaces.

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