Mapping Theorems for Rigid Continua and Their Inverse Limits

We give mapping theorems for certain families of rigid continua; i.e., we prove a mapping theorem for stars, paths and cycles of Cook continua. We also introduce the degree of rigidity of a continuum, the notion of 1 n -rigid continua and prove some existence theorems for 1 n -rigid continua. We als...

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Bibliographic Details
Published in:Qualitative theory of dynamical systems 2022-12, Vol.21 (4), Article 117
Main Authors: Banič, Iztok, Kac, Teja
Format: Article
Language:English
Subjects:
Difference and Functional Equations
Dynamical Systems and Ergodic Theory
Existence theorems
Mapping
Mathematics
Mathematics and Statistics
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Summary:We give mapping theorems for certain families of rigid continua; i.e., we prove a mapping theorem for stars, paths and cycles of Cook continua. We also introduce the degree of rigidity of a continuum, the notion of 1 n -rigid continua and prove some existence theorems for 1 n -rigid continua. We also construct a non-trivial infinite family of pairwise non-homeomorphic continua X with the property that for any sequence ( f n ) of continuous surjections f n : X → X , the inverse limit lim ← { X , f i } i = 1 ∞ is homeomorphic to X . Explicitly, we show that for each positive integer n , every 1 n -rigid continuum has this property.
ISSN:1575-5460
1662-3592
DOI:10.1007/s12346-022-00647-1