The Baire theorem, an analogue of the Banach fixed point theorem and attractors in T1 compact spaces

We prove that if X is a T1 second countable compact space, then X is a Baire space if and only if every nonempty open subset of X contains a closed subset with nonempty interior. We also prove an analogue of Banach's fixed point theorem for all T1 compact spaces. Applying the analogue of Banach...

Full description

Saved in:
Bibliographic Details
Published in:Bulletin des sciences mathématiques 2023-03, Vol.183, p.103231, Article 103231
Main Authors: Morayne, Michał, Rałowski, Robert
Format: Article
Language:English
Subjects:
[formula omitted] space
Attractor
Baire space
Compact space
Contraction
Fixed point
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We prove that if X is a T1 second countable compact space, then X is a Baire space if and only if every nonempty open subset of X contains a closed subset with nonempty interior. We also prove an analogue of Banach's fixed point theorem for all T1 compact spaces. Applying the analogue of Banach's fixed point theorem we prove the existence of unique attractors for so called contractive iterated function systems whose Hutchinson operators are closed in compact T1 spaces.
ISSN:0007-4497
1952-4773
DOI:10.1016/j.bulsci.2023.103231