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Compactification of a map which is mapped to itself

A. Iwanik, L. Janos, F. A. Smith

Published 2002-04-10Version 1

We prove that if $T: X \to X$ is a selfmap of a set $X$ such that $\bigcap \{T^{n}X: n\in N}\}$ is a one-point set, then the set $X$ can be endowed with a compact Hausdorff topology so that $T$ is continuous.

Comments: 5 pages
Journal: Proceedings of the Ninth Prague Topological Symposium, (Prague, 2001), pp. 165--169, Topology Atlas, Toronto, 2002
Categories: math.GN
Subjects: 54H20, 54H25
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