Extreme factorization of metrizability

We examine the three metrization theorems of Sakai, Tamano and Yajima in the context of my results on factorization of metrizability, the latter having been refined so that the former all follow similarly and immediately. We finish with a generalization of Sakai–Tamano–Yajima: On a topological space of countable pseudocharacter, availability of an LF-regular h-network is equivalent to metrizability.