This article is cited in 11 papers

Research Papers Dedicated to the 100th Anniversary of P. S. Alexandroff's Birth

On geometry of continuous mappings of countable functional weight

B. A. Pasynkov

M. V. Lomonosov Moscow State University

Abstract: 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.

UDC: 515.12

Received: 01.02.1997

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