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ON GRAEV’S THEOREM FOR FREE PRODUCTS OF HAUSDORFF TOPOLOGICAL GROUPS
Published online by Cambridge University Press: 29 March 2021
Abstract
The paper gives a simple proof of Graev’s theorem (asserting that the free product of Hausdorff topological groups is Hausdorff) for a particular case which includes the countable case of
$k_\omega $
-groups and the countable case of Lindelöf P-groups. For this it is shown that in these particular cases the topology of the free product of Hausdorff topological groups coincides with the
$X_0$
-topology in the Mal’cev sense, where X is the disjoint union of the topological groups identifying their units.
Keywords
MSC classification
- Type
- Research Article
- Information
- Bulletin of the Australian Mathematical Society , Volume 104 , Issue 3 , December 2021 , pp. 475 - 483
- Copyright
- © 2021 Australian Mathematical Publishing Association Inc.
Footnotes
The second author gratefully acknowledges the financial support from Shota Rustaveli Georgian National Science Foundation (Ref. FR-18-10849).
References
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