Axiom:Axiom of K-Approximation

Definition
Let $\left({S, \preceq}\right)$ be an ordered set.

Axiom of K-approximation says
 * $\forall x \in S: x = \sup \left({x^{\mathrm{compact} } }\right)$

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