Finiteness properties for self-similar continua

Abstract

We consider self-similar continua possessing finite intersection property and prove intersection graph criterion for self-similar dendrites, finite order Theorem for such continua satisfying open set condition in ${\mathbb{R}}^n$ and parameter matching Theorem which states that all Jordan arcs starting from a intersection point in such continuum on a plane should have the same slope parameter at that point.

arXiv comment14 pages