TY - JOUR
AU - Sun, Taixiang
AU - Li, Lue
AU - Su, Guangwang
AU - Han, Caihong
AU - Xia, Guoen
PY - 2020/10/01
Y2 - 2024/05/26
TI - The depth and the attracting centre for a continuous map on a fuzzy metric interval
JF - Applied General Topology
JA - Appl. Gen. Topol.
VL - 21
IS - 2
SE -
DO - 10.4995/agt.2020.13126
UR - https://ojs.upv.es/index.php/AGT/article/view/13126
SP - 285-294
AB - <p>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) = âˆªxâˆˆIω(x, f), ωn+1(f) = âˆªxâˆˆωn(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.</p>
ER -