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Semigroup closures of finite rank symmetric inverse semigroups |
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| Authors: | Oleg Gutik Jimmie Lawson Du?an Repov? |
| Institution: | (1) Department of Mechanics and Mathematics, Ivan Franko Lviv National University, Universytetska 1, Lviv, 79000, Ukraine;(2) Department of Mathematics, Louisiana State University, Baton Rouge, LA 70803, USA;(3) Institute of Mathematics, Physics and Mechanics, Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, Ljubljana, 1000, Slovenia |
| Abstract: | We introduce the notion of semigroup with a tight ideal series and investigate their closures in semitopological semigroups, particularly inverse semigroups with continuous inversion. As a corollary we show that the symmetric inverse semigroup of finite transformations I λ n of the rank ≤ n is algebraically closed in the class of (semi)topological inverse semigroups with continuous inversion. We also derive related results about the nonexistence of (partial) compactifications of classes of semigroups that we consider. |
| Keywords: | Topological semigroup Semitopological semigroup Topological inverse semigroup Symmetric inverse semigroup of finite transformations Algebraically closed semigroup ω -unstable set Semigroup with a tight ideal series |
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