Theorems · Theorem · algebraic topology

isQuotientCoveringMap_iff_isCoveringMap_and

∀ {E : Type u_1} {X : Type u_2} [inst : TopologicalSpace E] [inst_1 : TopologicalSpace X] (f : E → X) (G : Type u_3)
  [inst_2 : Group G] [inst_3 : MulAction G E],
  IsQuotientCoveringMap f G ↔
    IsCoveringMap f ∧
      Function.Surjective f ∧
        ContinuousConstSMul G E ∧ IsCancelSMul G E ∧ ∀ {e₁ e₂ : E}, f e₁ = f e₂ ↔ e₁ ∈ MulAction.orbit G e₂

Defined in

Mathlib.Topology.Covering.Quotient

Cited by

0 results in Mathlib

Foundations

Depth 90 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpaceGroupMulAction