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ON GRAEV’S THEOREM FOR FREE PRODUCTS OF HAUSDORFF TOPOLOGICAL GROUPS

Published online by Cambridge University Press:  29 March 2021

GURAM SAMSONADZE
Affiliation:
Georgian Technical University, 77 Kostava Str., Tbilisi0160, Georgia e-mail: g.samsonadze@gtu.ge
DALI ZANGURASHVILI*
Affiliation:
Andrea Razmadze Mathematical Institute, Tbilisi State University, 6 Tamarashvili Str., Tbilisi0177, Georgia

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.

Type
Research Article
Copyright
© 2021 Australian Mathematical Publishing Association Inc.

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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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ON GRAEV’S THEOREM FOR FREE PRODUCTS OF HAUSDORFF TOPOLOGICAL GROUPS
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