# Openly factorizable spaces and compact extensions of topological semigroups - Mathematics > General Topology

Abstract: We prove that the semigroup operation of a topological semigroup $S$ extendsto a continuous semigroup operation on its the Stone-\v{C}ech compactification$\beta S$ provided $S$ is a pseudocompact openly factorizable space, whichmeans that each map $f:S\to Y$ to a second countable space $Y$ can be writtenas the composition $f=g\circ p$ of an open map $p:X\to Z$ onto a secondcountable space $Z$ and a map $g:Z\to Y$. We present a spectralcharacterization of openly factorizable spaces and establish some properties ofsuch spaces.

Author: Taras Banakh, Svetlana Dimitrova

Source: https://arxiv.org/