Subcover
= Subcover
{title2=$J\subseteq I,\quad K\subseteq\bigcup_{j\in J}U_j$}
A <subcover> of an <open cover> $\{U_i:i\in I\}$ of a <subset> $K$ is a selection of its members whose <union> still contains $K$. The selected <open sets> retain their original sizes; selecting a <subcover> does not mean replacing them by smaller <open sets>.