Extremal topologies on groups

I.V.Protasov

We present some new constructions of refinements of a left invariant topology on a group. On one hand, these refinements are very close to the original topology of the group. On the other hand, these refinements have a wide spectrum of extremal topological properties.

1. Hindman N., Strauss D. Algebra in the Stone- Cech compactifications, De Gruyter Exposition in Mathematics. Vol. 27, 1998.

2. Hindman N., Protasov I., Strauss D. Topologies on $S$ determined by idempotent in $\be S$, Topology Proc. 23 (1998), 155--190.

3. Malykhin V. I. Extremely disconnected and similar groups, Soviet Math. Dokl. 16 (1975), 21–25. (in Russian)

4. Papazyan T. Extremal topologies on semigroup, Topol. Appl. 39 (1991), 229–243.

5. Протасов И. В. Фильтры и топологии на полугруппах, Мат. Студії, 3 (1994), 15–28.

6. Protasov I. V. Maximal topologies on groups, Sib. Math. Zh. 39 (1998), 1368–1381.

7. Protasov I. Combinatorics of Numbers, Math. Stud. Monogr. Ser., Vol.2. VNTL Publishers, 1997.

8. Протасов И. В. Идеалы полугруппы ультрафильтров топологической группы, Укр. Мат. Журн. 47 (1995), № 4, 506–511.

9. Протасов И. В. Ультрафильтры и топологии на группах, Сиб. Мат. Журн. 34 (1993), № 5, 163–180.

10. Протасов И. В. Неразложимые топологии на группах, Укр. мат.ё журн. 50 (1998), № 12, 1646–1655.

11. Protasov I. V. Equations in $\beta G$ and resolvability of Abelian groups, Math. Zam. (to appear).

12. Protasov I. V. Points of joint continuity for the semigroup of ultrafilters of Abelian group, Sbornik: Mathematics. 187 (1996), № 2, 287–296.

13. Сирота С. Произведения топологических групп и экстремальная несв'язность, Мат. сборник, 79 (1969), № 2, 179–192.

	Extremal topologies on groups
Author	I.V.Protasov Kyiv National University
Abstract	We present some new constructions of refinements of a left invariant topology on a group. On one hand, these refinements are very close to the original topology of the group. On the other hand, these refinements have a wide spectrum of extremal topological properties.
Keywords	new constructions, refinements, left invariant topology, group, original topology, extremal topological properties
DOI	doi:10.30970/ms.15.1.9-22
Reference	1. Hindman N., Strauss D. Algebra in the Stone- Cech compactifications, De Gruyter Exposition in Mathematics. Vol. 27, 1998. 2. Hindman N., Protasov I., Strauss D. Topologies on $S$ determined by idempotent in $\be S$, Topology Proc. 23 (1998), 155--190. 3. Malykhin V. I. Extremely disconnected and similar groups, Soviet Math. Dokl. 16 (1975), 21–25. (in Russian) 4. Papazyan T. Extremal topologies on semigroup, Topol. Appl. 39 (1991), 229–243. 5. Протасов И. В. Фильтры и топологии на полугруппах, Мат. Студії, 3 (1994), 15–28. 6. Protasov I. V. Maximal topologies on groups, Sib. Math. Zh. 39 (1998), 1368–1381. 7. Protasov I. Combinatorics of Numbers, Math. Stud. Monogr. Ser., Vol.2. VNTL Publishers, 1997. 8. Протасов И. В. Идеалы полугруппы ультрафильтров топологической группы, Укр. Мат. Журн. 47 (1995), № 4, 506–511. 9. Протасов И. В. Ультрафильтры и топологии на группах, Сиб. Мат. Журн. 34 (1993), № 5, 163–180. 10. Протасов И. В. Неразложимые топологии на группах, Укр. мат.ё журн. 50 (1998), № 12, 1646–1655. 11. Protasov I. V. Equations in $\beta G$ and resolvability of Abelian groups, Math. Zam. (to appear). 12. Protasov I. V. Points of joint continuity for the semigroup of ultrafilters of Abelian group, Sbornik: Mathematics. 187 (1996), № 2, 287–296. 13. Сирота С. Произведения топологических групп и экстремальная несв'язность, Мат. сборник, 79 (1969), № 2, 179–192.
Pages	9-22
Volume	15
Issue	1
Year	2001
Journal	Matematychni Studii
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