Category:Order Generating Subsets

This category contains results about Order Generating Subsets.

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

Let $X$ be a subset of $S$.

Then $X$ is order generating if and only if:

$\forall x \in S: x^\succeq \cap X$ admits an infimum and $x = \map \inf {x^\succeq \cap X}$