Has a coarser separable metrizable topology or Has a separable metrizable compression
The topology contains a coarser topology which is both Separable and Metrizable.
N.B. if the space is also $T_{3 \frac{1}{2}}$, by page 54 of DOI 10.1007/BFb0098389 this is equivalent to the function space being Separable.