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Equality of Dimensions for Some Paracompact \sigma$$-Spaces
Mathematical Notes
Mathematical Notes
It is proved that if X is a normal space which admits a closed fiberwise strongly zero-dimensiona... more It is proved that if X is a normal space which admits a closed fiberwise strongly zero-dimensional continuous map onto a stratifiable space Y in a certain class (an S-space), then Ind X = dim X. This equality also holds if Y is a paracompact σ-space and ind Y = 0. It is shown that any closed network of a closed interval or the real line is an S-network. A simple proof of the Katˇetov-Morita inequality for paracompact σ-spaces (and, hence, for stratifiable spaces) is given.
О размерности прообразов некоторых паракомпактных пространств
Matematicheskie Zametki, 2018
Equality of Dimensions for Some Paracompact \sigma$$-Spaces
Mathematical Notes
Mathematical Notes
It is proved that if X is a normal space which admits a closed fiberwise strongly zero-dimensiona... more 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 Ind X = dim X. 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 Katˇetov-Morita inequality for paracompact σ-spaces (and, hence, for stratifiable spaces) is given.
О размерности прообразов некоторых паракомпактных пространств
Matematicheskie Zametki, 2018