Characterization of compact subsets of curves with ω-continuous derivatives

Marcin Pilipczuk. "Characterization of compact subsets of curves with ω-continuous derivatives." Fundamenta Mathematicae 211.2 (2011): 175-195. <http://eudml.org/doc/282619>.

@article{MarcinPilipczuk2011,
abstract = { We give a characterization of compact subsets of finite unions of disjoint finite-length curves in ℝⁿ with ω-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. },
author = {Marcin Pilipczuk},
journal = {Fundamenta Mathematicae},
keywords = {curve with -continuous derivative; Jones's theorem; Whitney's theorem; unions of disjoint finite-length curves; compact set; Ahlfors-regular curves},
language = {eng},
number = {2},
pages = {175-195},
title = {Characterization of compact subsets of curves with ω-continuous derivatives},
url = {http://eudml.org/doc/282619},
volume = {211},
year = {2011},
}

TY - JOUR
AU - Marcin Pilipczuk
TI - Characterization of compact subsets of curves with ω-continuous derivatives
JO - Fundamenta Mathematicae
PY - 2011
VL - 211
IS - 2
SP - 175
EP - 195
AB - We give a characterization of compact subsets of finite unions of disjoint finite-length curves in ℝⁿ with ω-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.
LA - eng
KW - curve with -continuous derivative; Jones's theorem; Whitney's theorem; unions of disjoint finite-length curves; compact set; Ahlfors-regular curves
UR - http://eudml.org/doc/282619
ER -