Theorems · Theorem · algebraic topology

isAddQuotientCoveringMap_iff

∀ {E : Type u_1} {X : Type u_2} [inst : TopologicalSpace E] [inst_1 : TopologicalSpace X] (f : E → X) (G : Type u_3)
  [inst_2 : AddGroup G] [inst_3 : AddAction G E],
  IsAddQuotientCoveringMap f G ↔
    Topology.IsQuotientMap f ∧
      ContinuousConstVAdd G E ∧
        (∀ {e₁ e₂ : E}, f e₁ = f e₂ ↔ e₁ ∈ AddAction.orbit G e₂) ∧
          ∀ (e : E), ∃ U ∈ nhds e, ∀ (g : G), ((fun x => g +ᵥ x) '' U ∩ U).Nonempty → g = 0

Defined in

Mathlib.Topology.Covering.Quotient

Cited by

1 results in Mathlib

Foundations

Depth 22 from the axioms · uses propext, Quot.sound

Assumes

TopologicalSpaceTopologicalSpaceAddGroupAddAction