This is joint work with Carl Mummert. We initiate the reverse mathematics of general topology. We show that a certain metrization theorem is equivalent to Π_{2}^{1} comprehension. An MF space is defined to be a topological space of the form MF (P) with topology generated by N_{p}|p ∈ P. Here P is a poset, MF (P) is the set of maximal filters on P, and N_{p} = F ∈ MF (P)|p ∈ F. If the poset P is countable, the space MF (P) is said to be countably based. The class of countably based MF spaces can be defined and discussed within the subsystem ACA_{0} of second order arithmetic. One can prove within ACA_{0} that every complete separable metric space is homeomorphic to a countably based MF space which is regular. We show that the converse statement, “every countably based MF space which is regular is homeomorphic to a complete separable metric space,” is equivalent to Π_{2}^{1} − CA_{0}. The equivalence is proved in the weaker system Π_{1}^{1} − CA_{0}. This is the first example of a theorem of core mathematics which is provable in second order arithmetic and implies Π_{2}^{1} comprehension.