I believe a question is incorrectly worded, but I could be wrong as well.
I tried searching for an errata for Ahlfors Complex Analysis but was unable to find one. On page 63, question 2, it ask:
Show that the Heine-Borel property can also be expressed in the following manner: Every collection of closed sets with an empty intersection contains a finite subcollection with empty intersection.
Shouldn't it be worded either as
A topological space is compact iff every family of closed subsets having the finite intersection property satisfies $\cap F\neq\varnothing$ where the finite intersection property is $\cap F_{\alpha}\neq \varnothing$ for all finite subcollections $F_{\alpha}\subset F$.
or worded as
A space $X$ is compact iff every collection of closed subsets of $X$ with the finite intersection property has a nonempty intersection.
It is an equivalent statement. Loosely the statement FIP implies non empty intersection is the same as empty intersection implies not FIP.