I PRIKLADNAYA MATEMATIKA
(FUNDAMENTAL AND APPLIED MATHEMATICS)
1998, VOLUME 4, NUMBER 1, PAGES 155-164
B. A. Pasynkov
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A continuous mapping
$f\colon\, X \to Y$is parallel to a space $Z$if it is embeddable into the projection of the topological product $Y\times Z$onto $Y$. The theorems of W. Hurewicz (on the existence of a zero-dimensional continuous mapping into $k$-cubefor any $k$-dimensionalmetrizable compactum) and of N\"obeling--Pontrjagin--Lefschetz (on the embeddability of any $k$-dimensionalmetrizable compactum into $(2k+1)$-cube)are extended to continuous mappings of countable functional weight (i. e.\ mappings parallel to the Hilbert cube) of finite-dimensional (in sense of $\dim$) Tychonoff spaces.
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Last modified: April 8, 1998