Complement of Element is Irreducible implies Element is Meet Irreducible

Theorem
Let $T = \left({S, \tau}\right)$ be a topological space.

Let $P = \left({\tau, \preceq}\right)$ be an ordered set where $\mathord\preceq = \mathord\subseteq \cap \left({\tau \times \tau}\right)$

Let $A \in \tau$.

Then $\complement_S\left({A}\right)$ is irreducible implies $A$ is meet irreducible in $P$