Arcwise connectedness of the boundaries of connected self-similar sets
General Topology
2007-05-23 v1 Classical Analysis and ODEs
Abstract
Let T be the attractor of injective contractions f_1,...,f_m on R^2 that satisfy the Open Set Condition. If T is connected, \partial T is arcwise connected. In particular, the boundary of the Levy dragon is arcwise connected.
Cite
@article{arxiv.math/0302279,
title = {Arcwise connectedness of the boundaries of connected self-similar sets},
author = {Tai-Man Tang},
journal= {arXiv preprint arXiv:math/0302279},
year = {2007}
}
Comments
6 pages, no figure