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ON GRAEV’S THEOREM FOR FREE PRODUCTS OF HAUSDORFF TOPOLOGICAL GROUPS
- Source :
- Bulletin of the Australian Mathematical Society. 104:475-483
- Publication Year :
- 2021
- Publisher :
- Cambridge University Press (CUP), 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.
Details
- ISSN :
- 17551633 and 00049727
- Volume :
- 104
- Database :
- OpenAIRE
- Journal :
- Bulletin of the Australian Mathematical Society
- Accession number :
- edsair.doi...........4cabc2e2d18f45867cb7e8c81672c0c2