= Cover
{disambiguate=topology}
{title2=$E\subseteq\bigcup_iU_i$}
{wiki}
= Cover
{synonym}
= Cover of a set
{synonym}
A cover of a <set> $E$ is a family of <sets> whose <union> contains $E$. The members may overlap and may include points outside $E$; intersecting each member with $E$ gives a cover by its <subsets>. An <open cover> requires its members to be <open sets>. In <Hausdorff measure>, <countable> covers with a bound on each member's <diameter> determine geometric size. Constructing one inexpensive <cover> supplies an upper bound, while a lower bound must control all allowed <covers>.
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