Topological Structure of QWG(f) Set

Abstract

According to the definition of quasiweak almost periodic point, we introduce the definition of QWG(f) in the paper. We studied topological structure of G-quasiweak almost periodic point set. We have the following two results: (1) Let (Y,d′) be a compact G–metric space and f : X → X be equicontinuous. Let {fn}∞n=1 be G-strongly uniform converge to the map f and xk ∈ QWG(fn). If limk → ∞ xk = x, then x ∈ QWG(f); (2) Let (Y,d′) be a compact G-metric space and f : X → X be equicontinuous. If {fn}∞n=1 is G-strongly uniform converge to f, then we have lim sup QWG(fn) ⊂ QWG(f). The conclusions results generalize the corresponding results given in [Journal of Southwest China Normal University: Natural Science Edition 44(2019), 40-44].