\begin{definition}[Definition:Refinement of Cover/Coarser Cover]
Let $S$ be a set.
Let $\UU = \set {U_\alpha}$ and $\VV = \set {V_\beta}$ be covers of $S$.
Let $\VV$ be a refinement of $\UU$.
Then $\UU$ is '''coarser''' than $\VV$.
Category:Definitions/Covers
\end{definition}