Theorems · Theorem · algebraic topology

Topology.IsQuotientMap.isCoveringMapOn_of_smul_disjoint

∀ {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) →
        (∀ (e : E), ∃ U ∈ nhds e, ∀ (g : G), ((fun x => g • x) '' U ∩ U).Nonempty → g • e = e) →
          IsCoveringMapOn f (f '' {e | MulAction.stabilizer G e = ⊥})

Defined in

Mathlib.Topology.Covering.Quotient

Cited by

2 results in Mathlib

Foundations

Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpaceGroupMulActionContinuousConstSMul