On dimensionally restricted maps

H. Murat Tuncali; Vesko Valov

Fundamenta Mathematicae, Tome 173 (2002), p. 35-52 / Harvested from The Polish Digital Mathematics Library

Résumé

Let f: X → Y be a closed n-dimensional surjective map of metrizable spaces. It is shown that if Y is a C-space, then: (1) the set of all maps g: X → ⁿ with dim(f △ g) = 0 is uniformly dense in C(X,ⁿ); (2) for every 0 ≤ k ≤ n-1 there exists an $F_{σ}$ -subset $A_{k}$ of X such that $d i m A_{k} \leq k$ and the restriction $f | (X ∖ A_{k})$ is (n-k-1)-dimensional. These are extensions of theorems by Pasynkov and Toruńczyk, respectively, obtained for finite-dimensional spaces. A generalization of a result due to Dranishnikov and Uspenskij about extensional dimension is also established.

Publié le : 2002-01-01

Zbl 1021.54027

EUDML-ID : urn:eudml:doc:283094

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     year = {2002},
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H. Murat Tuncali; Vesko Valov. On dimensionally restricted maps. Fundamenta Mathematicae, Tome 173 (2002) pp. 35-52. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm175-1-2/