The depth and the attracting centre for a continuous map on a fuzzy metric interval

• Sun, Taixiang ^[1] ; Li, Lue ^[1] ; Su, Guangwang ^[1] ; Han, Caihong ^[1] ; Xia, Guoen ^[1]
  1. [1] Guangxi University of Finance and Economics

     Guangxi University of Finance and Economics

     China

     
• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 21, Nº. 2, 2020, págs. 285-294
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • Let I be a fuzzy metric interval and f be a continuous map from I to I. Denote by R(f), Ω(f) and ω(x, f) the set of recurrent points of f, the set of non-wandering points of f and the set of ω- limit points of x under f, respectively. Write ω(f) = ∪x∈Iω(x, f), ωn+1(f) = ∪x∈ωn(f)ω(x, f) and Ωn+1(f) = Ω(f|Ωn(f)) for any positive integer n. In this paper, we show that Ω2(f) = R(f) and the depth of f is at most 2, and ω3(f) = ω2(f) and the depth of the attracting centre of f is at most 2.