  Let $M$ be an orientable connected closed surface and $f$ be an $R$-closed
homeomorphism on $M$ which is isotopic to identity. Then the suspension of $f$
satisfies one of the following condition: 1) the closure of each element of it
is minimal and toral. 2) there is a minimal set which is not locally connected.
Moreover, we show that any positive iteration of an $R$-closed homeomorphism on
a compact metrizable space is $R$-closed.
