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On dimensionally restricted maps

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Tuncali H., Valov V.

Fundamenta Mathematicae

2002

tom 175

nr 1

35-52

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 → 𝕀ⁿ with dim(f △ g) = 0 is uniformly dense in C(X,𝕀ⁿ); (2) for every 0 ≤ k ≤ n-1 there exists an $F_{σ}$-subset $A_{k}$ of X such that $dim A_{k} ≤ k$ 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.

Ograniczanie wyników

1 Fundamenta Mathematicae

1 Tuncali H.

1 Valov V.

1 2002

Wyniki wyszukiwania

On dimensionally restricted maps