Topological semigroups of matrix units and countably compact Brandt $λ^0$-extensions of topological semigroups - Mathematics > Group TheoryReport as inadecuate




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Abstract: We show that a topological semigroup of finite partial bijections$\mathscr{I} \lambda^n$ of an infinite set with a compact subsemigroup ofidempotents is absolutely $H$-closed and any countably compact topologicalsemigroup does not contain $\mathscr{I} \lambda^n$ as a subsemigroup. We givesufficient conditions onto a topological semigroup $\mathscr{I} \lambda^1$ tobe non-$H$-closed. Also we describe the structure of countably compact Brandt$\lambda^0$-extensions of topological monoids and study the category ofcountably compact Brandt $\lambda^0$-extensions of topological monoids withzero.



Author: Oleg Gutik, Kateryna Pavlyk, Andriy Reiter

Source: https://arxiv.org/



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