Positively expansive homeomorphisms on compact metric spaces (Q625969)

The following theorem is known. Let \(X\) be a compact metric space. Then a homeomorphism \(h\colon X\rightarrow X\) is positively expansive if and only if \(X\) is expansive. In this paper a new and simple proof of the theorem is given. The main part of the new proof is the proof of the following result. Let \(X\) be a compact metric space containing infinitely many points. Then no homeomorphism \(h\colon X\rightarrow X\) is positively expansive.