compact space and intersection of closed sets

Let \((X, \mathcal{T})\) be a topological space. TFAE:

1. \(X\) is compact, as in there exists a finite subcover
2. for closed sets \(A_i \subseteq X\) with \(\bigcap A_i = \emptyset\) there exist finitely many \(A_i\) such that \(\bicgap_{i=1}^n A_i = \emptyset\)

consequence of allgemeine de Morgansche Gesetz (Mengenlehre)