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 $A \subseteq F(A)$?
A question about a continuous function on a compact metric space
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metric-spaces
compactness
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0What is the need for compactness in your question? – 2012-11-16