On Whitney pairs

Volume 160 / 1999

Marianna Csörnyei Fundamenta Mathematicae 160 (1999), 63-79 DOI: 10.4064/fm-160-1-63-79


A simple arc ϕ is said to be a Whitney arc if there exists a non-constant function f such that   $lim_{x ↦ x_0} (|f(x)-f(x_0)|)/(|ϕ(x)-ϕ(x_0)|) = 0$ for every $x_0$. G. Petruska raised the question whether there exists a simple arc ϕ for which every subarc is a Whitney arc, but for which there is no parametrization satisfying   $lim_{t ↦ t_0} (|t-t_0|)/(|ϕ(t)-ϕ(t_0)|) = 0$. We answer this question partially, and study the structural properties of possible monotone, strictly monotone and VBG* functions f and associated Whitney arcs.


  • Marianna Csörnyei

Search for IMPAN publications

Query phrase too short. Type at least 4 characters.

Rewrite code from the image

Reload image

Reload image