On Finite-Dimensional Maps II

Details On Finite-Dimensional Maps II On Finite-Dimensional Maps II

2002-02-12

arxiv.org/abs/math/0202114v4

Mathematics

General Topology

8 pages

Scientific paper

Let $f\colon X\to Y$ be a perfect $n$-dimensional surjection of paracompact
spaces with $Y$ being a $C$-space. We prove that, for any $m\geq n+1$, almost
all (in the sense of Baire category) maps $g$ from $X$ into the $m$-dimensional
cube have the following property: $g(f^{-1}(y))$ is at most $n$-dimensional for
every $y\in Y$.

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