A Note on Almost Periodic Points and Minimal Sets in T1- and T2-Spaces

Abstract

We show that (1) there exist almost periodic orbits in T2-spaces of which the closures are not minimal sets; (2) there exist minimal sets in locally compact T1-spaces which are not compact; (3) there exist almost periodic orbits in T2-spaces of which the closures contain not only almost periodic points. These give answers to the three problems given by Mai and Sun in (2007).