Finite-to-one maps and dimension

• Autorzy: Jerzy Krzempek
• Języki publikacji: EN

Abstrakty

EN

It is shown that for every at most k-to-one closed continuous map f from a non-empty n-dimensional metric space X, there exists a closed continuous map g from a zero-dimensional metric space onto X such that the composition f∘g is an at most (n+k)-to-one map. This implies that f is a composition of n+k-1 simple ( = at most two-to-one) closed continuous maps. Stronger conclusions are obtained for maps from Anderson-Choquet spaces and ones that satisfy W. Hurewicz's condition (α). The main tool is a certain extension of the Lebesgue-Čech dimension to finite-to-one closed continuous maps.

Kategorie tematyczne

• 54C10: Special maps on topological spaces (open, closed, perfect, etc.)
• 54F45: Dimension theory
• 54E40: Special maps on metric spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2004
• Tom: 182
• Numer: 2
• Strony: 95-106

Daty

wydano

2004

Twórcy

autor

Jerzy Krzempek

• Institute of Mathematics, Silesian University of Technology, Kaszubska 23, 44-100 Gliwice, Poland

Identyfikatory

DOI

10.4064/fm182-2-1