Mathlib Map

Theorems · Theorem · general topology

Homeomorph.coe_trans

∀ {α : Type u_1} {β : Type u_2} {γ : Type u_3} [inst : TopologicalSpace α] [inst_1 : TopologicalSpace β]
  [inst_2 : TopologicalSpace γ] (f : α ≃ₜ β) (g : β ≃ₜ γ), ↑(f.trans g) = (↑g).comp ↑f
Defined in
Mathlib.Topology.ContinuousMap.Basic
Cited by
2 results in Mathlib
Foundations
Depth 17 from the axioms · uses Quot.sound
Assumes
TopologicalSpaceTopologicalSpaceTopologicalSpace
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

Homeomorph.symm_comp_toContinuousMap · cited by 1Homeomorph.symm_comp_toCo…Homeomorph.toContinuousMap_comp_symm · cited by 1Homeomorph.toContinuousMa…TopologicalSpace · cited by 24529TopologicalSpaceContinuousMap · cited by 2491ContinuousMapHomeomorph · cited by 725HomeomorphContinuousMap.comp · cited by 181ContinuousMap.comptoContinuousMap · cited by 99toContinuousMapHomeomorph.trans · cited by 49Homeomorph.transHomeomorph.coe_transCITED BYCITES

Cites6

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

Cited by2

Results whose statement or proof uses this declaration.