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

Taras Banakh; Dusan Repovs

paper

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

arXiv:0911.3985

Abstract

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.

arXiv comment20 pages