α : Type u
γ : Type u_1
inst✝¹ : TopologicalSpace γ
inst✝ : T2Space γ
f : α → γ
this : TopologicalSpace α := ⊥
⊢ Ultrafilter.extend f ∘ pure = f
α : Type u
γ : Type u_1
inst✝¹ : TopologicalSpace γ
inst✝ : T2Space γ
f : α → γ
⊢ Ultrafilter.extend f ∘ pure = f
letI : TopologicalSpace α := ⊥
α : Type u
γ : Type u_1
inst✝¹ : TopologicalSpace γ
inst✝ : T2Space γ
f : α → γ
this✝ : TopologicalSpace α := ⊥
this : DiscreteTopology α
⊢ Ultrafilter.extend f ∘ pure = f
α : Type u
γ : Type u_1
inst✝¹ : TopologicalSpace γ
inst✝ : T2Space γ
f : α → γ
this : TopologicalSpace α := ⊥
⊢ Ultrafilter.extend f ∘ pure = f
haveI : DiscreteTopology α := ⟨rfl⟩
no goals
α : Type u
γ : Type u_1
inst✝¹ : TopologicalSpace γ
inst✝ : T2Space γ
f : α → γ
this✝ : TopologicalSpace α := ⊥
this : DiscreteTopology α
⊢ Ultrafilter.extend f ∘ pure = f
exact funext (denseInducing_pure.extend_eq continuous_of_discreteTopology)