Abstract

Let f be a continuous map of the circle S1 into itself. And let R(f),Λ(f),Γ(f), and Ω(f) denote the set of recurrent points, ω-limit points, γ-limit points, and nonwandering points of f, respectively. In this paper, we show that each point of Ω(f)\R(f)¯ is one-side isolated, and prove that(1) Ω(f)\Γ(f) is countable and(2) Λ(f)\Γ(f) and R(f)¯\Γ(f) are either empty or countably infinite.