α : Type u_2
β : Type u_1
inst✝² : TopologicalSpace α
inst✝¹ : TopologicalSpace β
f : α → β
inst✝ : SecondCountableTopology β
hf : Inducing f
⊢ SecondCountableTopology α
α : Type u_2
β : Type u_1
inst✝² : TopologicalSpace α
inst✝¹ : TopologicalSpace β
f : α → β
inst✝ : SecondCountableTopology β
hf : Inducing f
⊢ SecondCountableTopology α
rw [hf.1]
no goals
α : Type u_2
β : Type u_1
inst✝² : TopologicalSpace α
inst✝¹ : TopologicalSpace β
f : α → β
inst✝ : SecondCountableTopology β
hf : Inducing f
⊢ SecondCountableTopology α
exact secondCountableTopology_induced α β f