Theorems · Definition · general topology

Homeomorph.smulOfNeZero

{α : Type u_2} →
  {G₀ : Type u_4} →
    [inst : TopologicalSpace α] →
      [inst_1 : GroupWithZero G₀] → [inst_2 : MulAction G₀ α] → [ContinuousConstSMul G₀ α] → (c : G₀) → c ≠ 0 → α ≃ₜ α

Scalar multiplication by a non-zero element of a group with zero acting on α is a homeomorphism from α onto itself.

Defined in

Mathlib.Topology.Algebra.ConstMulAction

Cited by

11 results in Mathlib

Foundations

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

Assumes

TopologicalSpaceGroupWithZeroMulActionContinuousConstSMul