Ultrafilters and non-Cantor minimal sets in linearly ordered dynamical systems
By a discrete dynamical system \((X,\varphi)\) is understood a continuous selfmap \(\varphi: X\to X\) of a Tychonoff space \(X\) into itself. A subset \(M\subseteq X\) is said to be minimal for \(\varphi\) if it is a minimal element in the set partially ordered by inclusion of all nonempty closed \(\varphi\)-invariant sets \(A\subseteq X\). As their main result the authors exhibit \(2^c\) nonhomeomorphic, nonmetrizable minimal sets in a compact connected linearly ordered dynamical system.
scientific article; zbMATH DE number 5313045