Symmetric inverse topological semigroups of finite rank ≤n
Анотація
We establish topological properties of the symmetric inverse topological semigroup of finite transformations \mathcal Iλn of the rank ≤n. We show that the topological inverse semigroup \mathcal Iλn 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 Iλn for infinite cardinal λ and show that the Bohr compactification of an infinite topological symmetric inverse semigroup of finite transformations \mathcal Iλn of the rank ≤n is the trivial semigroup.
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