Abstract. Let f be a continuous map of the circle S 1 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 thatare either empty or countably infinite.
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