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For each of the following statements, either give a proof of exhibit a counterexample.

If $x$ is an accumulation point of $T$, then $x$ is an accumulation point of each set $A$ in $F$.

False. $T$ could be the set $\{x\}$ and $x$ may only be a point in some of $A_n$. Correct?

If $x$ is an accumulation point of $S$, then $x$ is an accumulation point of at least one set $A$ in $F$.

Not sure but wouldn't $x$ have to be an accumulation point of all $A$?