Abstract
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 IndX = dimX. This equality also holds if Y is a paracompact σ-space and 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 Kateˇ tov–Morita inequality for paracompact σ-spaces (and, hence, for stratifiable spaces) is given.
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Original Russian Text © I. M. Leibo, 2018, published in Matematicheskie Zametki, 2018, Vol. 103, No. 3, pp. 404–416.
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Leibo, I.M. On the Dimension of Preimages of Certain Paracompact Spaces. Math Notes 103, 405–414 (2018). https://doi.org/10.1134/S0001434618030070
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DOI: https://doi.org/10.1134/S0001434618030070