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arXiv · 0911.3985

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

Taras Banakh·Dusan Repovs
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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.

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Taras Banakh, Dusan Repovs. 2009-11-20. Direct limit topologies in the categories of topological groups and of uniform spaces. https://arxiv.org/abs/0911.3985

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