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Let $M$ be an orientable connected closed surface and $f$ be an $R$-closedhomeomorphism 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 itis 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 ona compact metrizable space is $R$-closed.

Toral or non locally connected minimal sets for suspensions of $R$-closed surface homeomorphisms