FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(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 $\$f:\; X\; \to \; Y\$$ 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.

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Last modified: April 8, 1998