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<p>and lower bounds. Therefore, a set of real numbers is bounded if it is contained in a <a href="page.php?w=interval_%28mathematics%29">finite interval</a>.</p>

<p><big> Definition in a metric space </big></p>
<p>A <a href="page.php?w=subset">subset</a>  of a <a href="page.php?w=metric_space">metric space</a>  is <b>bounded</b> if there exists  such that for all  and  in , we have . The metric space  is a bounded metric space (or  is a bounded metric) if  is bounded as a subset of itself.</p>

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*<a href="page.php?w=Total_boundedness">Total boundedness</a></p><p>
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