Let （X,d） be a compact metric space and f:X→X be continuous. We say that f is pointwise periodic, if for each x∈X, there exists an integer n（x）>0 such that f(n（x）（x）=x, that is, P（f）=X. We say that f is periodic, if there exists some integer n>0 such that fn=id, that is, fn is identity.
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