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<p>analogous statement is <a href="page.php?w=sequential_compactness">sequential compactness</a>: a set is compact if and only if every <a href="page.php?w=infinite_sequence">infinite sequence</a> in the set has a <a href="page.php?w=subsequence">subsequence</a> that converges to a point of the set. Likewise, whereas every real-valued function on a finite set is bounded and attains its maximum and minimum, every <a href="page.php?w=continuous_function">continuous</a> real-valued function on a compact space has these properties. For compact subsets</p><p>
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