Theorems · Theorem · algebraic topology

IsCoveringMap.liftPath_apply_one_eq_of_homotopicRel

∀ {E : Type u_1} {X : Type u_2} [inst : TopologicalSpace E] [inst_1 : TopologicalSpace X] {p : E → X}
  (cov : IsCoveringMap p) {γ₀ γ₁ : C(↑unitInterval, X)},
  γ₀.HomotopicRel γ₁ {0, 1} →
    ∀ (e : E) (h₀ : γ₀ 0 = p e) (h₁ : γ₁ 0 = p e), (cov.liftPath γ₀ e h₀) 1 = (cov.liftPath γ₁ e h₁) 1

Lifting two paths that are homotopic relative to {0,1} starting from the same point also ends up in the same point.

Defined in

Mathlib.Topology.Homotopy.Lifting

Cited by

1 results in Mathlib

Foundations

Depth 129 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpace