A note on Hutchinson operator in T₁ compact topological spaces

2023/03/12 by Michał Morayne, Morayne, Michał, Robert Rałowski +1
Mathematics · #Fixed Point Theorems Analysis

paper · pdf · doi:10.48550/arxiv.2303.06767

Abstract

In T₁ compact topological spaces the Hutchinson operator of a contractive IFS (iterated function system; a finite family of closed mappings from the space into itself) may not be closed. Nevertheless, the Hutchinson operator of a contractive IFS has always a unique fixed point.

Related

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• On the continuity of the Hutchinson operator
• The Hutchinson-Barnsley theory for infinite iterated function systems
• Contractive Families on Compact Spaces
• A characterization of compact operators via the non-connectedness of the attractors of a family of IFSs