Definition:Coarser Subset (Order Theory)

Definition
Let $L = \struct {S, \preceq}$ be a preordered set.

Let $X, Y$ be subsets of $S$.

Then $X$ is coarser (subset) than $Y$
 * $\forall x \in X: \exists y \in Y: y \preceq x$

Also See

 * Definition:Finer Subset (Order Theory)