Mathlib Map

Theorems · Definition · general topology

Path.mul

{X : Type u_1} →
  [inst : TopologicalSpace X] →
    [inst_1 : Mul X] → [ContinuousMul X] → {a₁ b₁ a₂ b₂ : X} → Path a₁ b₁ → Path a₂ b₂ → Path (a₁ * a₂) (b₁ * b₂)

Pointwise multiplication of paths in a topological group.

Defined in
Mathlib.Topology.Path
Cited by
3 results in Mathlib
Foundations
Depth 123 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
TopologicalSpaceMulContinuousMul
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Joined.mul · cited by 2Joined.mulJoinedIn.mul · cited by 1JoinedIn.mulPath.mul_apply · cited by 0Path.mul_applyTopologicalSpace · cited by 24529TopologicalSpaceContinuousMul · cited by 343ContinuousMulPath · cited by 318Pathcontinuous_mul · cited by 41continuous_mulPath.map · cited by 21Path.mapPath.prod · cited by 9Path.prodPath.mulCITED BYCITES

Cites6

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by3

Results whose statement or proof uses this declaration.