Theorems · Theorem · algebraic topology

IsCoveringMap.constOn_of_comp

∀ {E : Type u_1} {X : Type u_2} [inst : TopologicalSpace E] [inst_1 : TopologicalSpace X] {f : E → X},
  IsCoveringMap f →
    ∀ {A : Type u_3} [inst_2 : TopologicalSpace A] {s : Set A} {g : A → E},
      IsPreconnected s →
        ContinuousOn g s → (∀ a ∈ s, ∀ a' ∈ s, f (g a) = f (g a')) → ∀ {a a' : A}, a ∈ s → a' ∈ s → g a = g a'

Defined in

Mathlib.Topology.Covering.Basic

Cited by

0 results in Mathlib

Foundations

Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpaceTopologicalSpace