Czasopismo
Tytuł artykułu
Autorzy
Warianty tytułu
Języki publikacji
Abstrakty
A simple arc γ ⊂ ℝⁿ is called a Whitney arc if there exists a non-constant real function f on γ such that $lim_{y→x, y∈γ} |f(y)-f(x)|/|y-x| = 0$ for every x ∈ γ; γ is 1-critical if there exists an f ∈ C¹(ℝⁿ) such that f'(x) = 0 for every x ∈ γ and f is not constant on γ. We show that the two notions are equivalent if γ is a quasiarc, but for general simple arcs the Whitney property is weaker. Our example also gives an arc γ in ℝ² each of whose subarcs is a monotone Whitney arc, but which is not a strictly monotone Whitney arc. This answers completely a problem of G. Petruska which was solved for n ≥ 3 by the first author in 1999.
Słowa kluczowe
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
119-130
Opis fizyczny
Daty
wydano
2008
Twórcy
autor
- Department of Mathematics, University College London, Gower Street, London, WC1E 6BT, United Kingdom
autor
- Department of Mathematical Sciences, Florida Atlantic University, 777 Glades Road, Boca Raton, FL 33431, U.S.A.
autor
- Department of Mathematical Analysis, Charles University, Sokolovská 83, 186 75 Praha 8, Czech Republic
Bibliografia
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_4064-fm199-2-2