Openly factorizable spaces and compact extensions of topological semigroups

Taras O. Banakh; Svetlana Dimitrova

Commentationes Mathematicae Universitatis Carolinae (2010)

  • Volume: 51, Issue: 1, page 113-131
  • ISSN: 0010-2628

Abstract

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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.

How to cite

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Banakh, Taras O., and Dimitrova, Svetlana. "Openly factorizable spaces and compact extensions of topological semigroups." Commentationes Mathematicae Universitatis Carolinae 51.1 (2010): 113-131. <http://eudml.org/doc/37747>.

@article{Banakh2010,
abstract = {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 $f:S\rightarrow Y$ to a second countable space $Y$ can be written as the composition $f=g\circ p$ of an open map $p:X\rightarrow Z$ onto a second countable space $Z$ and a map $g:Z\rightarrow Y$. We present a spectral characterization of openly factorizable spaces and establish some properties of such spaces.},
author = {Banakh, Taras O., Dimitrova, Svetlana},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {topological semigroup; semigroup compactification; inverse spectrum; pseudocompact space; openly factorizable space; openly generated space; Eberlein compact; Corson compact; Valdivia compact; topological semigroup; extension of operation to compactification},
language = {eng},
number = {1},
pages = {113-131},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Openly factorizable spaces and compact extensions of topological semigroups},
url = {http://eudml.org/doc/37747},
volume = {51},
year = {2010},
}

TY - JOUR
AU - Banakh, Taras O.
AU - Dimitrova, Svetlana
TI - Openly factorizable spaces and compact extensions of topological semigroups
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2010
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 51
IS - 1
SP - 113
EP - 131
AB - 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 $f:S\rightarrow Y$ to a second countable space $Y$ can be written as the composition $f=g\circ p$ of an open map $p:X\rightarrow Z$ onto a second countable space $Z$ and a map $g:Z\rightarrow Y$. We present a spectral characterization of openly factorizable spaces and establish some properties of such spaces.
LA - eng
KW - topological semigroup; semigroup compactification; inverse spectrum; pseudocompact space; openly factorizable space; openly generated space; Eberlein compact; Corson compact; Valdivia compact; topological semigroup; extension of operation to compactification
UR - http://eudml.org/doc/37747
ER -

References

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