FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

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

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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Last modified: April 8, 1998