Resolvability of $\tau$-bounded groups

Protasov I.V

It is constructed a partition of an infinite group $G=A_1\cup A_2$ such that the subsets $A_1$, $A_2$ are dense in any totally bounded group topology. It is proposed some generalization of this construction.

1. Comfort W.W., van Mill J. Groups with only resolvable group topologies, Proc. Amer. Math. Soc. 1994. V.120. No 3. P.687–696.

2. Протасов И.В. Дискретные подмножества топологических групп, Матем. заметки. 1994, Т.55. No 1. С.150–151.

3. Berhanu S., Comfort W.W., Reid J.D. Counting subgroups and topological group topologies, Pacific J. Math. 1985. V.116. P.217–241.

4. Гуран И.И. О топологических группах, близких к финально компактным, Докл. АН СССР. Т.256. No 6. С.1305–1307.

5. Протасов И.В. Ультрафильтры и топологии на группах, Сиб. мат. журн. 1993. Т.34. No 5. С.163–180. Department of Cybernetics, Kiev University, pr. Glushkova, 6, Kiev, Ukraine

	Resolvability of $\tau$-bounded groups
Author	Protasov I.V
Abstract	It is constructed a partition of an infinite group $G=A_1\cup A_2$ such that the subsets $A_1$, $A_2$ are dense in any totally bounded group topology. It is proposed some generalization of this construction.
Keywords	tau-bounded groups, topological group, infinite group, Amenable group, groups resolvability
DOI	doi:10.30970/ms.5.1.17-20
Reference	1. Comfort W.W., van Mill J. Groups with only resolvable group topologies, Proc. Amer. Math. Soc. 1994. V.120. No 3. P.687–696. 2. Протасов И.В. Дискретные подмножества топологических групп, Матем. заметки. 1994, Т.55. No 1. С.150–151. 3. Berhanu S., Comfort W.W., Reid J.D. Counting subgroups and topological group topologies, Pacific J. Math. 1985. V.116. P.217–241. 4. Гуран И.И. О топологических группах, близких к финально компактным, Докл. АН СССР. Т.256. No 6. С.1305–1307. 5. Протасов И.В. Ультрафильтры и топологии на группах, Сиб. мат. журн. 1993. Т.34. No 5. С.163–180. Department of Cybernetics, Kiev University, pr. Glushkova, 6, Kiev, Ukraine
Pages	17-20
Volume	5
Issue	1
Year	1995
Journal	Matematychni Studii
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