Tohoku Mathematical Journal
2012
March
SECOND SERIES VOL. 64, NO. 1

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

Title DIRECT LIMIT TOPOLOGIES IN THE CATEGORIES OF TOPOLOGICAL GROUPS AND OF UNIFORM SPACES

Author Taras Banakh and Dušan Repovš

(Received December 4, 2009, revised May 28, 2010)
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.

2000 Mathematics Subject Classification. Primary 22A05; Secondary 18A30; 54B30; 54E15; 54H11.
Key words and phrases. Direct limit, topological group, uniform space.

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