Axiom:Axiom of K-Approximation

Definition
Let $\struct {S, \preceq}$ be an ordered set.

The axiom of $K$-approximation says
 * $\forall x \in S: x = \map \sup {x^{\mathrm{compact} } }$

where $x^{\mathrm{compact} }$ denotes the compact closure of $x$.