Compact Orbit and Topological Sensitivity on Locally Compact Spaces
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A cover-based notion of topological sensitivity and sensitivity at a point is introduced, which is the same as the popular concept of sensitivity in metric spaces. The basin of attraction of infinity, the point of compactification of locally compact, non-compact topological spaces, is studied in this paper. It is proved that, under certain conditions on the underlying map f , the set of points whose orbits have compact support, the basin of attraction of infinity, and the set of sensitive points are identical, thus generalizing the standard Julia sets on the Riemann sphere.