# $M$-mappings make their images less cellular

Commentationes Mathematicae Universitatis Carolinae (1994)

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

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topTkachenko, 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

top- ArhangelskiĭA.V., Factorization theorems and function spaces: stability and monolithicity, Soviet Math. Dokl. 26 (1982), 177-181. (1982)
- ArhangelskiĭA.V., Ranchin D.V., On dense subspaces of topological products and properties related with final compactness (in Russian), Vestnik Mosc. Univ. 1982, No.6, 21-28.
- Engelking R., On functions defined on cartesian products, Fund. Math. 59 (1966), 221-231. (1966) Zbl0158.41203MR0203697
- Hušek M., Productivity of properties of topological groups, Topology Appl. 44 (1992), 189-196. (1992) MR1173257
- Juhász I., Cardinal Functions in Topology, Math. Centrum Tracts 34, Amsterdam, 1971. MR0340021
- Kombarov A.P., Malykhin V.I., On $\Sigma $-products (in Russian), Dokl. AN SSSR 213 (1973), 774-776. (1973) MR0339073
- Maltsev A.I., To the general theory of algebraic systems (in Russian), Mat. Sb. 35 (1954), 3-20. (1954) MR0065533
- Nagami K., $\Sigma $-spaces, Fund. Math. 65 (1969), 169-192. (1969) Zbl0181.50701MR0257963
- Pasynkov B.A., On the relative cellularity of Lindelöf subspaces of topological groups, Topol. Appl., to appear. Zbl0803.54016MR1278026
- Tkačenko M.G., Some results on inverse spectra. I., Comment. Math. Univ. Carolinae 22 (1981), 621-633. (1981) MR0633589
- Tkačenko M.G., On the Souslin property in free topological groups over compacta (in Russian), Matem. Zametki 34 (1983), 601-607. (1983) MR0722229
- Tkačenko M.G., On mappings improving properties of their images (in Russian), Uspekhi Matem. Nauk 48 (1993), 187-188. (1993)
- Tkačenko M.G., $M$-spaces and the cellularity of spaces, Topology Appl., to appear.
- Todorčević S., Remarks on cellularity in products, Compositio Math. 57 (1986), 357-372. (1986) MR0829326
- Todorčević S., Cellularity of topological groups, Handwritten notes.
- UspenskiĭV.V., Topological group generated by a Lindelöf $\Sigma $-space has the Souslin property, Soviet Math. Dokl. 26 (1982), 166-169. (1982)
- UspenskiĭV.V., On continuous images of Lindelöf topological groups (in Russian, translated in English), Dokl. AN SSSR 285 (1985), 824-827. (1985) MR0821360
- UspenskiĭV.V., The Maltsev operation on countably compact spaces, Comment. Math. Univ. Carolinae 30 (1989), 395-402. (1989) MR1014140

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