\begin{definition}[Definition:Countable Finite Intersection Axiom]
Let $T = \struct {S, \tau}$ be a topological space.
Let $T$ be such that:
:Every countable set $V_\alpha$ of closed sets of $T$ such that $\ds \bigcap V_\alpha = \O$ contains a finite subset $V_\beta \subseteq V_\alpha$ such that $\ds \bigcap V_\beta = \O$.
Then $T$ satisfies the '''countable finite intersection axiom'''.
\end{definition}