The continuity of the inversion and the structure of maximal subgroups in countably compact topological semigroups

被引：0
|
作者：
O. Gutik
D. Pagon
D. Repovš
机构：
[1] Ivan Franko Lviv National University,Department of Mechanics and Mathematics
[2] Universytetska 1,Institute of Mathematics, Physics and Mechanics, and Faculty of Natural Sciences and Mathematics
[3] University of Maribor,Faculty of Mathematics and Physics, and Faculty of Education
[4] University of Ljubljana,undefined
来源：
Acta Mathematica Hungarica | 2009年 / 124卷
关键词：
topological semigroup; topological inverse semigroup; sequential space; sequentially compact space; countably compact space; pseudocompact space; regular space; quasi-regular space; subgroup; closure; inversion; paratopological group; topological group; Clifford semigroup; topologically periodic semigroup; MA; selective ultrafilter; primary 22A15, 54H10, 54D55; secondary 22A05, 54D30, 54D40;
D O I：
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学科分类号：
摘要：
We search for conditions on a countably compact (pseudocompact) topological semigroup under which: (i) each maximal subgroup H(e) in S is a (closed) topological subgroup in S; (ii) the Clifford part H(S) (i.e. the union of all maximal subgroups) of the semigroup S is a closed subset in S; (iii) the inversion inv: H(S) → H(S) is continuous; and (iv) the projection π: H(S) → E(S), π: x ↦ xx−1, onto the subset of idempotents E(S) of S, is continuous.
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页码：201 / 214
页数：13
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