| Title:
|
Openly factorizable spaces and compact extensions of topological semigroups (English) |
| Author:
|
Banakh, Taras |
| Author:
|
Dimitrova, Svetlana |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
51 |
| Issue:
|
1 |
| Year:
|
2010 |
| Pages:
|
113-131 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We prove that the semigroup operation of a topological semigroup $S$ extends to a continuous semigroup operation on its Stone-Čech 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. (English) |
| Keyword:
|
topological semigroup |
| Keyword:
|
semigroup compactification |
| Keyword:
|
inverse spectrum |
| Keyword:
|
pseudocompact space |
| Keyword:
|
openly factorizable space |
| Keyword:
|
openly generated space |
| Keyword:
|
Eberlein compact |
| Keyword:
|
Corson compact |
| Keyword:
|
Valdivia compact |
| MSC:
|
22A15 |
| MSC:
|
54B30 |
| MSC:
|
54C08 |
| MSC:
|
54C20 |
| MSC:
|
54D35 |
| idZBL:
|
Zbl 1224.54043 |
| idMR:
|
MR2666084 |
| . |
| Date available:
|
2010-05-21T12:37:20Z |
| Last updated:
|
2013-09-22 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140089 |
| . |
| Reference:
|
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