Contractive function systems, their attractors and metrization

TL;DR

This paper extends the Hutchinson-Barnsley fractal theory to multimetric and topological spaces, establishing connections between these frameworks and exploring their implications for attractors and metrization.

Contribution

It introduces a unified approach to fractal theory in multimetric and topological spaces, bridging the gap between these perspectives.

Findings

Established links between multimetric and topological fractal frameworks

Extended attractor concepts to broader space classes

Provided insights into metrization within fractal theory

Abstract

In this paper we study the Hutchinson-Barnsley theory of fractals in the setting of multimetric spaces (which are sets endowed with point separating families of pseudometrics) and in the setting of topological spaces. We find natural connections between these two approaches.