  We introduce a new way of encoding general topology in second order
arithmetic that we call hybrid maximal filter (hybrid MF) spaces. This notion
is a modification of the notion of a proper MF space introduced by Montalb\'an.
We justify the shift by showing that proper MF spaces are not able to code most
topological spaces, while hybrid MF spaces can code any second countable MF
space. We then answer Montalb\'an's question about metrization of well-behaved
MF spaces to this shifted context. To be specific, we show that in stark
contrast to the original MF formalization used by Mummert and Simpson, the
metrization theorem can be proven for hybrid MF spaces within $\text{ACA}_0$
instead of needing $\Pi_2^1-\text{CA}_0$.
