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\section{Introduction}

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\Prove: a set is closed if and only if it contains all its limit points given that
\(1) a point is said to be a limit point of \(\Omega\) and if there exists a sequence of points \(Z_n\in\Omega\) such that \(Z_n \ne Z\) and \(\lim_{x \to \infty} Z_n=Z\)
\(2) a set \(\Omega\) is closed if its complement \(\Omega^c = C-\Omega\)
\(3) a set \(\Omega\) is open if every point in that set is an interior point of \(\Omega\)
\(4) a point is an interior point of \(\Omega \subset C\) if there exists \(r > 0\) such that \(D_r(Z_0) \subset \Omega\)

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