User:Dfeuer/Definition:Complete Meet Subsemilattice

Definition

Let $(S, \preceq)$ be an ordered set.

Let $C \subseteq S$.

Then $C$ is a complete meet subsemilattice (of $S$) iff:

For each $D \subseteq C$:

$D$ has an infimum in $S$

$\inf D \in C$