Abstract
We prove that if the bilateral uniformity B of a topological group of pointwise countable type is complete, then the Hausdorff–Bourbaki uniformity of B is complete. It follows that for every Čech complete topological group, the Hausdorff–Bourbaki uniformity of B is complete. Finally, we prove that if X is a compact topological space, then the Hausdorff–Bourbaki uniformity of the bilateral uniformity of the free Abelian topological group over X, is complete.
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