## Tohoku Mathematical Journal

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

#### Abstract

Given an increasing sequence $(G_n)$ of topological groups, we study the topologies of the direct limits of the sequence $(G_n)$ in the categories of topological groups and of uniform spaces and find conditions under which these two direct limit topologies coincide.

#### Article information

Source
Tohoku Math. J. (2), Volume 64, Number 1 (2012), 1-24.

Dates
First available in Project Euclid: 26 March 2012

Permanent link to this document
https://projecteuclid.org/euclid.tmj/1332767338

Digital Object Identifier
doi:10.2748/tmj/1332767338

Mathematical Reviews number (MathSciNet)
MR2911130

Zentralblatt MATH identifier
1241.22002

#### Citation

Banakh, Taras; Repovš, Dušan. Direct limit topologies in the categories of topological groups and of uniform spaces. Tohoku Math. J. (2) 64 (2012), no. 1, 1--24. doi:10.2748/tmj/1332767338. https://projecteuclid.org/euclid.tmj/1332767338