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Let $S^*$ be the set of condensation points of $S$, and $S'$ be the set of cluster points of $S$ . Give an example of $S$ such that $S^{**}$ is not equal to $S^*$ and an example of $S$ such that $S^*$ is neither contained in nor contains $(S')^*$.

P.S. The problem comes with a hint which suggests considering space of functions $\left[a,b\right]$ to $\left[0,1\right]$ with sup metric and the set of "delta-functions with rational values", of which I have no idea.

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