On the Continuity of Inversion in Countably Compact Inverse Topological Semigroups

被引：0

作者：

Taras O. Banakh

Oleg V. Gutik

机构：

[1] Instytut Matematyki Akademia Swietokrzyska,

[2] Kielce Swietokrzyska,undefined

[3] 15 Kielce,undefined

[4] Poland and Department of Mathematics,undefined

[5] Ivan Franko Lviv National University,undefined

[6] Universytetska 1 Lviv,undefined

[7] 79000,undefined

[8] Department of Algebra,undefined

[9] Pidstrygach Institute for Applied Problems of Mechanics and Mathematics,undefined

[10] National Academy of Sciences Naukova 3b Lviv,undefined

[11] 79060,undefined

[12] Ukraine and Department of Mathematics,undefined

[13] Ivan Franko Lviv National University,undefined

[14] Universytetska 1 Lviv,undefined

[15] 79000,undefined

来源：

Semigroup Forum | 2004年 / 68卷

关键词：

Inverse Semigroup; Hausdorff Space; Continuous Semigroup; Compact Hausdorff Space; Topological Semigroup;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

Let S be a countably compact Hausdorff space endowed with a continuous semigroup operation turning S into an inverse semigroup. It is shown that the inversion inv : x ↦ x-1 in S is continuous provided one of the following conditions is satisfied: (1) the space S is sequential, (2) the semigroup S is Clifford, inversely regular, and topologically periodic, (3) the semigroup S is Clifford, topologically periodic and the square S × S is regular and countably compact. These results are close to the best possible since there is an example of a quasi-regular sequentially compact commutative inverse topological semigroup with discontinuous inversion.

引用

页码：411 / 418

页数：7