Uncountable Family of 0-Rigid Continua that are Homeomorphic to Their Inverse Limits

• Matevž Crepnjak ^[1] ; Teja Kac ^[1]
  1. [1] University of Maribor

     University of Maribor

     Eslovenia

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 22, Nº 2, 2023
• Idioma: inglés
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• Resumen

  • It is a well-known fact that there are continua X such that the inverse limit of any inverse sequence {X, fn} with surjective continuous bonding functions fn is homeomorphic to X. The pseudoarc or any Cook continuum are examples of such continua. Recently, a large family of continua X was constructed in such a way that X is 1 m -rigid and the inverse limit of any inverse sequence {X, fn} with surjective continuous bonding functions fn is homeomorphic to X by Baniˇc and Kac. In this paper, we construct an uncountable family of pairwise non-homeomorphic continua X such that X is 0-rigid and prove that for any sequence ( fn) of continuous surjections on X, the inverse limit lim ←−{X, fn} is homeomorphic to X.