On geometry of continuous mappings of countable functional weight

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 Nöbeling–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.