UCL Discovery

Abstract

A simple are phi is said to be a Whitney are if there exists a non-constant function f such thatlim(x-->x0) \f(x)-f(x(0))\ / \phi(x)-phi(x(0))\ = 0for every to. G. Petruska raised the question whether there exists a simple are phi for which every subarc is a Whitney are, but for which there is no parametrization satisfyinglim(t-->t0) \t-t(0)\ / \phi(t)-phi(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.