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The Set of {omega}-Limit Points of A Map of the Circle is Closed

Authors:	Hero Michael W

Institution:	Department of Mathematics, Bradley University Peoria, IL 61625, USA

Abstract:	Let f be a continuous self-map of the unit circle, S¹. The ${omega}$ -limitpoints ${omega}$ (x) of a point x are the set of all limit points of thesequence of iterates of f acting on x. We shall show that theset of all ${omega}$ -limit points ${cup}$ _xS¹ ${omega}$ (x) a closed set in S¹.

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