Openly factorizable spaces and compact extensions of topological semigroups

Details Openly factorizable spaces and compact extensions of topological semigroups Openly factorizable spaces and compact extensions of topological semigroups

2008-11-26

arxiv.org/abs/0811.4272v1

Comment. Math. Univ. Carolin. Vol.51, No.1 (2010) 113-131

Mathematics

General Topology

13 pages

Scientific paper

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

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