General position theorem and its applications
Vladislav Aseev, Kirill Kamalutdinov, Andrei Tetenov
TL;DR
This paper presents generalized formulations of the position theorem for parametrized fractal families and demonstrates their use in establishing the existence of self-similar sets with specific properties.
Contribution
It introduces new general and special versions of the position theorem and applies them to construct self-similar fractals with desired characteristics.
Findings
Existence of self-similar sets with prescribed properties
New formulations of the general position theorem
Application techniques for fractal construction
Abstract
We introduce some general and special formulations of general position theorem for parametrized families of fractals and explain the techniques of its application to prove the existence of self-similar sets with prescribed special properties.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.