Maps with dimensionally restricted fibers

Vesko Valov

Colloquium Mathematicae, Tome 122 (2011), p. 239-248 / Harvested from The Polish Digital Mathematics Library

Résumé

We prove that if f: X → Y is a closed surjective map between metric spaces such that every fiber $f^{-1}(y)$ belongs to a class S of spaces, then there exists an $F_{σ}$-set A ⊂ X such that A ∈ S and $dim f^{-1}(y)∖A = 0$ for all y ∈ Y. Here, S can be one of the following classes: (i) M: e-dim M ≤ K for some CW-complex K; (ii) C-spaces; (iii) weakly infinite-dimensional spaces. We also establish that if S = M: dim M ≤ n, then dim f ∆ g ≤ 0 for almost all $g ∈ C(X,^{n+1})$.

Détail

Publié le : 2011-01-01

Zbl 1234.54041

EUDML-ID : urn:eudml:doc:286652