\begin{definition}[Definition:Axiom of K-Approximation]
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 $x$.
\end{definition}