Definition:Precise Refinement of Cover

Definition
Let:


 * $\SS = \set {S_\gamma: \gamma \in \Gamma}$

be a cover of a set $X$.

Also let:


 * $\TT = \set {T_\gamma: \gamma \in \Gamma}$

be a cover of $X$.

Then $\TT$ is a precise refinement of $\SS$ :


 * $\forall \gamma \in \Gamma: T_\gamma \subseteq S_\gamma$