Tohoku Mathematical Journal

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

Taras Banakh and Dušan Repovš

Full-text: Open access

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

Subjects
Primary: 22A05: Structure of general topological groups
Secondary: 18A30: Limits and colimits (products, sums, directed limits, pushouts, fiber products, equalizers, kernels, ends and coends, etc.) 54B30: Categorical methods [See also 18B30] 54E15: Uniform structures and generalizations 54H11: Topological groups [See also 22A05]

Keywords
Direct limit topological group uniform space

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


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