Theorems · Theorem · algebraic topology

Topology.IsQuotientMap.isQuotientCoveringMap_of_properlyDiscontinuousSMul

∀ {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],
  Topology.IsQuotientMap f →
    ∀ [ContinuousConstSMul G E],
      (∀ {e₁ e₂ : E}, f e₁ = f e₂ ↔ e₁ ∈ MulAction.orbit G e₂) →
        ∀ [ProperlyDiscontinuousSMul G E] [LocallyCompactSpace E] [T2Space E] [IsCancelSMul G E],
          IsQuotientCoveringMap f G

Defined in

Mathlib.Topology.Covering.Quotient

Cited by

1 results in Mathlib

Foundations

Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpaceGroupMulActionContinuousConstSMulProperlyDiscontinuousSMulLocallyCompactSpaceT2SpaceIsCancelSMul