Theorems · Definition · algebraic topology

IsQuotientCoveringMap.toPermFiber

{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 → (x : X) → G →* Equiv.Perm ↑(f ⁻¹' {x})

A quotient covering map f induces a permutation action on each fiber.

Defined in

Mathlib.Topology.Covering.Quotient

Cited by

11 results in Mathlib

Foundations

Depth 23 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpaceGroupMulAction