Openly factorizable spaces and compact extensions of topological semigroups
| Autor: | Banakh, Taras, Dimitrova, Svetlana |
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| Rok vydání: | 2008 |
| Předmět: | |
| Zdroj: | Comment. Math. Univ. Carolin. Vol.51, No.1 (2010) 113-131 |
| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: 13 pages |
| Databáze: | arXiv |
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