2010/11/17 by Annie Carter, Carter, Annie, Daniel Lithio +3
Computer Science · Mathematics · #Data Management and Algorithms #FOS: Mathematics #General Topology (math.GN) #Mathematical Dynamics and Fractals #Topological and Geometric Data Analysis #math.GN
paper · pdf · doi:10.48550/arxiv.1011.4026
Withdrawn due to some errors and new developments leading to a complete rewrite
openalex publication_date 2010/11/17 · arxiv created 2015/11/16 · arxiv updated 2015/11/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Much of the structure in metric spaces that allows for the creation of fractals exists in more generalized non-metrizable spaces. In particular the same theorems regarding the behavior of compact sets can be proven in the more general framework of β-spaces. However in most β-spaces, a set being compact (and more generally being totally bounded) is so restrictive as to render all fractal examples completely uninteresting. In this paper we provide a generalization of compact sets, continuous functions, and all the related machinery necessary for fractals to be defined as the unique fixed set of an IFS. We conclude by discussing some interesting examples of non-metrizable fractals.