\begin{definition}[Definition:Refinement of Cover/Finer 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 $\VV$ is '''finer''' than $\UU$.
Category:Definitions/Covers
\end{definition}