Discrete Dynamics in Nature and Society
Volume 2008 (2008), Article ID 262475, 5 pages
doi:10.1155/2008/262475

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

Jie-Hua Mai1 and Xin-He Liu2

1Institute of Mathematics, Shantou University, Shantou, Guangdong 515063, China
2Institute of Mathematics, Guangxi University, Nanning, Guangxi 530004, China

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).