Pełnotekstowe zasoby PLDML oraz innych baz dziedzinowych są już dostępne w nowej Bibliotece Nauki.
Zapraszamy na https://bibliotekanauki.pl

PL EN

Preferencje
Język
Widoczny [Schowaj] Abstrakt
Liczba wyników
• Artykuł - szczegóły

Fundamenta Mathematicae

2002 | 175 | 1 | 35-52

On dimensionally restricted maps

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.

35-52

wydano
2002

Twórcy

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