Maps with dimensionally restricted fibers

• Autorzy: Vesko Valov
• Języki publikacji: EN

Abstrakty

EN

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 $g ∈ C(X,𝕀^{n+1})$.

Kategorie tematyczne

• 54F45: Dimension theory
• 54E40: Special maps on metric spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2011
• Tom: 123
• Numer: 2
• Strony: 239-248

Daty

wydano

2011

Twórcy

autor

Vesko Valov

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

Identyfikatory

DOI

10.4064/cm123-2-8