(FUNDAMENTAL AND APPLIED MATHEMATICS)

1998, VOLUME 4, NUMBER 1, PAGES 155-164

## On geometry of continuous mappings of countable functional weight

B. A. Pasynkov

Abstract

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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 $k$-cube for any $k$-dimensional metrizable compactum) and of N\"obeling--Pontrjagin--Lefschetz (on the embeddability of any $k$-dimensional metrizable 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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