Theorems · Theorem · algebraic topology

Homeomorph.trans_toHomotopyEquiv

∀ {X : Type u} {Y : Type v} {Z : Type w} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y]
  [inst_2 : TopologicalSpace Z] (h₀ : X ≃ₜ Y) (h₁ : Y ≃ₜ Z),
  (h₀.trans h₁).toHomotopyEquiv = h₀.toHomotopyEquiv.trans h₁.toHomotopyEquiv

Defined in: Mathlib.Topology.Homotopy.Equiv
Cited by: 0 results in Mathlib
Foundations: Depth 127 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: TopologicalSpace TopologicalSpace TopologicalSpace

Mathlib docs Source Loogle LeanSearch

Around this declaration

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

Cites6

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

TopologicalSpacestatement and proof · cited by 24,529
Homeomorphstatement and proof · cited by 725
Homeomorph.transstatement · cited by 49
ContinuousMap.HomotopyEquivstatement · cited by 23
Homeomorph.toHomotopyEquivstatement · cited by 7
ContinuousMap.HomotopyEquiv.transstatement · cited by 6

Cited by0

Results whose statement or proof uses this declaration.

Nothing cites this yet.