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suppose that (X,d) is a compact metric space and $f:X\to X$ is a continuous function. Define $X_1 = f(X), X_2 = f(X_1),...,X_{i+1} = f(X_i),...$ and let $A = \bigcap_{i=1}^\infty X_i$. Is $A \subseteq F(A)$?

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    What is the need for compactness in your question?2012-11-16

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