Symmetric inverse topological se­mi­groups of fi­ni­te rank ≤n

Анотація

We establish topological properties of the symmetric inverse topological semigroup of finite transformations $\mathcal I$_λⁿ of the rank ≤n. We show that the topological inverse semigroup $\mathcal I$_λⁿ is algebraically h-closed in the class of topological inverse semigroups. Also we prove that a topological semigroup S with countably compact square S×S does not contain the semigroup $\mathcal I$_λⁿ for infinite cardinal λ and show that the Bohr compactification of an infinite topological symmetric inverse semigroup of finite transformations $\mathcal I$_λⁿ of the rank ≤n is the trivial semigroup.