M -mappings make their images less cellular

Mihail G. Tkachenko

Commentationes Mathematicae Universitatis Carolinae (1994)

  • Volume: 35, Issue: 3, page 553-563
  • ISSN: 0010-2628

Abstract

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We consider M -mappings which include continuous mappings of spaces onto topological groups and continuous mappings of topological groups elsewhere. It is proved that if a space X is an image of a product of Lindelöf Σ -spaces under an M -mapping then every regular uncountable cardinal is a weak precaliber for X , and hence X has the Souslin property. An image X of a Lindelöf space under an M -mapping satisfies c e l ω X ≤ 2 ω . Every M -mapping takes a Σ ( ℵ 0 ) -space to an ℵ 0 -cellular space. In each of these results, the cellularity of the domain of an M -mapping can be arbitrarily large.

How to cite

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Tkachenko, Mihail G.. "$M$-mappings make their images less cellular." Commentationes Mathematicae Universitatis Carolinae 35.3 (1994): 553-563. <http://eudml.org/doc/247603>.

@article{Tkachenko1994,
abstract = {We consider $M$-mappings which include continuous mappings of spaces onto topological groups and continuous mappings of topological groups elsewhere. It is proved that if a space $X$ is an image of a product of Lindelöf $\Sigma $-spaces under an $M$-mapping then every regular uncountable cardinal is a weak precaliber for $X$, and hence $ X$ has the Souslin property. An image $X$ of a Lindelöf space under an $M$-mapping satisfies $cel_\{\omega \}X\le 2^\{\omega \}$. Every $M$-mapping takes a $\Sigma (\aleph _0)$-space to an $\aleph _0$-cellular space. In each of these results, the cellularity of the domain of an $M$-mapping can be arbitrarily large.},
author = {Tkachenko, Mihail G.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {$M$-mapping; topological group; Maltsev space; $\aleph _0$-cellularity; Mal'tsev space; -cellularity; -mapping; -cellular space},
language = {eng},
number = {3},
pages = {553-563},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {$M$-mappings make their images less cellular},
url = {http://eudml.org/doc/247603},
volume = {35},
year = {1994},
}

TY - JOUR
AU - Tkachenko, Mihail G.
TI - $M$-mappings make their images less cellular
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1994
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 35
IS - 3
SP - 553
EP - 563
AB - We consider $M$-mappings which include continuous mappings of spaces onto topological groups and continuous mappings of topological groups elsewhere. It is proved that if a space $X$ is an image of a product of Lindelöf $\Sigma $-spaces under an $M$-mapping then every regular uncountable cardinal is a weak precaliber for $X$, and hence $ X$ has the Souslin property. An image $X$ of a Lindelöf space under an $M$-mapping satisfies $cel_{\omega }X\le 2^{\omega }$. Every $M$-mapping takes a $\Sigma (\aleph _0)$-space to an $\aleph _0$-cellular space. In each of these results, the cellularity of the domain of an $M$-mapping can be arbitrarily large.
LA - eng
KW - $M$-mapping; topological group; Maltsev space; $\aleph _0$-cellularity; Mal'tsev space; -cellularity; -mapping; -cellular space
UR - http://eudml.org/doc/247603
ER -

References

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