Minimal sets of R-closed surface homeomorphisms

Abstract: Let M be an orientable connected closed surface and f be a homeomorphism on M. Suppose that the set is closed. Then the suspension of f satisfies one of the following conditions: 1) the closure of each element of it is toral; 2) there is a minimal set which is not locally connected. Moreover, we show that if the set of a homeomorphism f on a compact metrizable space is closed, then so is for any natural number k. [Copyright &y& Elsevier]