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

被引：0
|
作者：
Samsonadze, Guram [1 ]
Zangurashvili, Dali [2 ]
机构：
[1] Georgian Tech Univ, 77 Kostava Str, Tbilisi 0160, Georgia
[2] Tbilisi State Univ, 6 Tamarashvili Str, Tbilisi 0177, Georgia
来源：
BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY | 2021年 / 104卷 / 03期
基金：
美国国家科学基金会;
关键词：
free product of Hausdorff topological groups; k(omega)-group; Lindelof P-group; Mal'cev initial topology;
D O I：
10.1017/S0004972721000137
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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 Lindelof 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.
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页码：475 / 483
页数：9
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