Geodesic
On the Dimension of Preimages of Certain Paracompact Spaces
Matematičeskie zametki, Tome 103 (2018) no. 3, pp. 404-416

Voir la notice de l'article provenant de la source Math-Net.Ru

It is proved that if $X$ is a normal space which admits a closed fiberwise strongly zero-dimensional continuous map onto a stratifiable space $Y$ in a certain class (an S-space), then $\operatorname{Ind}{X}=\operatorname{dim}{X}$. This equality also holds if ${Y}$ is a paracompact $\sigma$-space and $\operatorname{ind}{Y}=0$. It is shown that any closed network of a closed interval or the real line is an S-network. A simple proof of the Katětov–Morita inequality for paracompact $\sigma$-spaces (and, hence, for stratifiable spaces) is given.
Mots-clés : dimension, stratifiable space.
Keywords: network, $\sigma$-space 
@article{MZM_2018_103_3_a6,
     author = {I. M. Leibo},
     title = {On the {Dimension} of {Preimages} of {Certain} {Paracompact} {Spaces}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {404--416},
     publisher = {mathdoc},
     volume = {103},
     number = {3},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2018_103_3_a6/}
}
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I. M. Leibo. On the Dimension of Preimages of Certain Paracompact Spaces. Matematičeskie zametki, Tome 103 (2018) no. 3, pp. 404-416. http://geodesic.mathdoc.fr/item/MZM_2018_103_3_a6/