The free product of topological groups being Hausdorff is Hausdorff --- a new proof

Details The free product of topological groups being Hausdorff is Hausdorff --- a new proof The free product of topological groups being Hausdorff is Hausdorff --- a new proof

2010-07-28

arxiv.org/abs/1007.4887v1

Mathematics

General Topology

8 pages

Scientific paper

The explicit description of the topology of the free product of topological groups being Hausdorff is given. In particular, it is shown that it coincides with the so-called $X_0$-topology for the corresponding colimit $X$ in the category of topological spaces. Applying this fact, a new short proof of the well-known Graev's theorem asserting that the free product of topological groups being Hausdorff is Hausdorff is given.

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