Compactification of a map which is mapped to itself

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

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 topolog…