Theorems · Theorem · algebraic topology

IsLocalHomeomorph.continuous_lift

∀ {E : Type u_1} {X : Type u_2} {A : Type u_3} [inst : TopologicalSpace E] [inst_1 : TopologicalSpace X]
  [inst_2 : TopologicalSpace A] {p : E → X},
  IsLocalHomeomorph p →
    IsSeparatedMap p →
      ∀ (f : C(↑unitInterval × A, X)) {g : ↑unitInterval × A → E},
        p ∘ g = ⇑f → (Continuous fun x => g (0, x)) → (∀ (a : A), Continuous fun x => g (x, a)) → Continuous g

Defined in

Mathlib.Topology.Homotopy.Lifting

Cited by

1 results in Mathlib

Foundations

Depth 120 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpaceTopologicalSpace