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Symmetric inverse topological semigroups of finite rank $leqslant n$ | | Oleg Gutik
; Andriy Reiter
; | | Date: |
1 Dec 2009 | | Abstract: | We study topological properties of the symmetric inverse topological
semigroup of finite transformations $mathscr{I}_lambda^n$ of the rank
$leqslant n$. We show that the topological inverse semigroup
$mathscr{I}_lambda^n$ is algebraically $h$-closed in the class of topological
inverse semigroups. Also we prove that a topological semigroup $S$ with
countably compact square $S imes S$ does not contain the semigroup
$mathscr{I}_lambda^n$ for infinite cardinal $lambda$ and show that the Bohr
compactification of an infinite topological symmetric inverse semigroup of
finite transformations $mathscr{I}_lambda^n$ of the rank $leqslant n$ is the
trivial semigroup. | | Source: | arXiv, 0912.0198 | | Services: | Forum | Review | PDF | Favorites | |
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