Characterization of compact subsets of curves with $\omega$-continuous derivatives
Tom 211 / 2011
Fundamenta Mathematicae 211 (2011), 175-195
MSC: Primary 53A04.
DOI: 10.4064/fm211-2-4
Streszczenie
We give a characterization of compact subsets of finite unions of disjoint finite-length curves in $\mathbb R^n$ with $\omega$-continuous derivative and without self-intersections. Intuitively, our condition can be formulated as follows: there exists a finite set of regular curves covering a compact set $K$ iff every triple of points of $K$ behaves like a triple of points of a regular curve.
This work was inspired by theorems by Jones, Okikiolu, Schul and others that characterize compact subsets of rectifiable or Ahlfors-regular curves. However, their classes of curves are much wider than ours and therefore the condition we obtain and our methods are different.
