%0 Journal Article
%T Symmetric inverse topological semigroups of finite rank $\leqslant n$
%A Oleg Gutik
%A Andriy Reiter
%J Mathematics
%D 2009
%I arXiv
%X 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 $S\times S$ 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.
%U http://arxiv.org/abs/0912.0198v1