Geodesic
$M$-mappings make their images less cellular
Commentationes Mathematicae Universitatis Carolinae, Tome 35 (1994) no. 3, pp. 553-563 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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 $\Sigma$-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 $cel_{\omega}X\le2^{\omega}$. 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.
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 $cel_{\omega}X\le2^{\omega}$. 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.
Classification : 54A25, 54C99, 54H11
Keywords: $M$-mapping; topological group; Maltsev space; $\aleph_0$-cellularity 
@article{CMUC_1994_35_3_a13,
     author = {Tka\v{c}enko, Michael G.},
     title = {$M$-mappings make their images less cellular},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {553--563},
     year = {1994},
     volume = {35},
     number = {3},
     mrnumber = {1307283},
     zbl = {0840.54002},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_1994_35_3_a13/}
}
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Tkačenko, Michael G. $M$-mappings make their images less cellular. Commentationes Mathematicae Universitatis Carolinae, Tome 35 (1994) no. 3, pp. 553-563. http://geodesic.mathdoc.fr/item/CMUC_1994_35_3_a13/