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The continuity of the inversion and the structure of maximal subgroups in countably compact topological semigroups |
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| Authors: | O. Gutik D. Pagon D. Repovš |
| Affiliation: | (1) Department of Mechanics and Mathematics, Ivan Franko Lviv National University, Universytetska 1, Lviv, 79000, Ukraine;(2) Institute of Mathematics, Physics and Mechanics, and Faculty of Natural Sciences and Mathematics, University of Maribor, Gosposvetska 84, Maribor, 2000, Slovenia;(3) Faculty of Mathematics and Physics, and Faculty of Education, University of Ljubljana, P.O.B. 2964, Ljubljana, 1001, Slovenia |
| Abstract: | 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. |
| Keywords: | KeywordHeading" > and phrases 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 MAcountable selective ultrafilter |
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