On dimensionally restricted maps

• Autorzy: H. Murat Tuncali , Vesko Valov
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 55M10: Dimension theory
• 54C65: Selections
• 54F45: Dimension theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2002
• Tom: 175
• Numer: 1
• Strony: 35-52

Daty

wydano

2002

Twórcy

autor

H. Murat Tuncali

• Department of Mathematics, Nipissing University, 100 College Drive, P.O. Box 5002, North Bay, ON, P1B 8L7, Canada

autor

Vesko Valov

• Department of Mathematics, Nipissing University, 100 College Drive, P.O. Box 5002, North Bay, ON, P1B 8L7, Canada

Identyfikatory

DOI

10.4064/fm175-1-2