A note on Hutchinson operator in $\mathbf{T_1}$ compact topological spaces

A note on Hutchinson operator in $\mathbf{T_1}$ compact topological spaces

In $T_1$ 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.

Saved in:
Bibliographic Details
Main Authors: Morayne, Michał, Rałowski, Robert
Format: Journal Article
Language:English
Published: 12-03-2023
Subjects:
Mathematics - General Topology
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:In $T_1$ 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.
DOI:10.48550/arxiv.2303.06767