Wyniki wyszukiwania

Sortuj według:

Ogranicz wyniki do:

Whitney arcs and 1-critical arcs

100%

Csörnyei M., Kališ J., Zajíček L.

Fundamenta Mathematicae

2008

tom 199

nr 2

119-130

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.

Ograniczanie wyników

1 Fundamenta Mathematicae

1 Csörnyei M.

1 Kališ J.

1 Zajíček L.

1 2008

Wyniki wyszukiwania

Whitney arcs and 1-critical arcs