Geodesic
Equality of Dimensions for Some Paracompact
Matematičeskie zametki, Tome 113 (2023) no. 4, pp. 499-516

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The equality of the dimensions $\operatorname{Ind}X$ and $\operatorname{dim}X$ of a first countable paracompact $\sigma$-space $X$ with a 1-continuous semimetric is proved. A partial positive answer to A. V. Arkhangel'skii's question about the equality of dimensions for first countable spaces with a countable network is given. As a consequence, the equality of the dimensions $\operatorname{Ind}X$ and $\operatorname{dim}X$ for Nagata spaces (that is, stratifiable first countable spaces) with a 1-continuous semimetric is obtained.
Mots-clés : dimension, stratifiable space.
Keywords: network, $\sigma$-space 
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     author = {I. M. Leibo},
     title = {Equality of {Dimensions} for {Some} {Paracompact}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {499--516},
     publisher = {mathdoc},
     volume = {113},
     number = {4},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2023_113_4_a2/}
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I. M. Leibo. Equality of Dimensions for Some Paracompact. Matematičeskie zametki, Tome 113 (2023) no. 4, pp. 499-516. http://geodesic.mathdoc.fr/item/MZM_2023_113_4_a2/