Theorems · Theorem · algebraic topology

IsCoveringMap.injective_path_homotopic_map

∀ {E : Type u_1} {X : Type u_2} [inst : TopologicalSpace E] [inst_1 : TopologicalSpace X] {p : E → X}
  (cov : IsCoveringMap p) (e₀ e₁ : E), Function.Injective fun γ => γ.map { toFun := p, continuous_toFun := ⋯ }

A covering map induces an injection on all Hom-sets of the fundamental groupoid, in particular on the fundamental group. The first part of Proposition 1.31 of [hatcher02].

Defined in

Mathlib.Topology.Homotopy.Lifting

Cited by

0 results in Mathlib

Foundations

Depth 134 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpace