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Openly factorizable spaces and compact extensions of topological semigroups

Taras O. Banakh, Svetlana Dimitrova (2010)

Commentationes Mathematicae Universitatis Carolinae

We prove that the semigroup operation of a topological semigroup S extends to a continuous semigroup operation on its Stone-Čech compactification β S provided S is a pseudocompact openly factorizable space, which means that each map f : S Y to a second countable space Y can be written as the composition f = g p of an open map p : X Z onto a second countable space Z and a map g : Z Y . We present a spectral characterization of openly factorizable spaces and establish some properties of such spaces.

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