theorem PiBase.Homeomorph.metrizableSpace {X : Type u_1} {Y : Type u_2} [TopologicalSpace X] [TopologicalSpace Y] [h : TopologicalSpace.MetrizableSpace X] (f : X ≃ₜ Y) : TopologicalSpace.MetrizableSpace Y

theorem PiBase.WellDefined.metrizableSpace : WellDefined TopologicalSpace.MetrizableSpace