Equicontinuous local dendrite maps

• Salem, Aymen Haj ^[1] ; Hattab, Hawete ^[2] ; Rejeiba, Tarek ^[1]
  1. [1] Sfax University
  2. [2] Umm Alqura University Makkah
• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 22, Nº. 1, 2021, págs. 67-77
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • Let X be a local dendrite, and f : X → X be a map. Denote by E(X) the set of endpoints of X. We show that if E(X) is countable, then the following are equivalent:(1) f is equicontinuous;(2)  fn (X) = R(f);(3) f|  fn (X) is equicontinuous;(4) f| fn (X) is a pointwise periodic homeomorphism or is topologically conjugate to an irrational rotation of S 1 ;(5) ω(x, f) = Ω(x, f) for all x ∈ X.This result generalizes [17, Theorem 5.2], [24, Theorem 2] and [11, Theorem 2.8].