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Compactification of a map which is mapped to itself

A. Iwanik·L. Janos·F. A. Smith
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Abstract

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.

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A. Iwanik, L. Janos, F. A. Smith. 2002-04-10. Compactification of a map which is mapped to itself. https://arxiv.org/abs/math/0204131

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