Topological and ditopological unosemigroups

Author T. Banakh, I. Pastukhova,
Ivan Franko National University of Lviv

Abstract In this paper we introduce and study a new topologo-algebraic structure called a (di)topological unosemigroup. This is a topological semigroup endowed with continuous unary operations of left and right units (which have certain continuous division property called the dicontinuity). We show that the class of ditopological unosemigroups contains all topological groups, all topological semilattices, all uniformizable topological unosemigroups, all compact topological unosemigroups, and is closed under the operations of taking subunosemigroups, Tychonoff product, reduced product, semidirect product, and the Hartman-Mycielski extension.
Keywords topological semigroup; unosemigroup; ditopological unosemigroup
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Pages 119-133
Volume 39
Issue 2
Year 2013
Journal Matematychni Studii
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