Theorems · Definition · general topology
Homeomorph.sumArrowHomeomorphProdArrow
{X : Type u_1} → [inst : TopologicalSpace X] → {ι : Type u_7} → {ι' : Type u_8} → (ι ⊕ ι' → X) ≃ₜ (ι → X) × (ι' → X)The natural homeomorphism (ι ⊕ ι' → X) ≃ₜ (ι → X) × (ι' → X).
Equiv.sumArrowEquivProdArrow as a homeomorphism.
- Defined in
- Mathlib.Topology.Homeomorph.Lemmas
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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
- Equivproof · cited by 8,337
- Homeomorphstatement · cited by 725
- Equiv.sumArrowEquivProdArrowproof · cited by 9
Cited by10
Results whose statement or proof uses this declaration.
- GenLoop.currySumproof · cited by 4
- GenLoop.genLoopGenLoopEquivproof · cited by 2
- CommRingCat.HomTopology.isEmbedding_pushoutproof · cited by 0
- GenLoop.continuous_currySumproof · cited by 0
- GenLoop.currySum_apply_coestatement · cited by 0
- Homeomorph.sumArrowHomeomorphProdArrow_applystatement and proof · cited by 0
- Homeomorph.sumArrowHomeomorphProdArrow_symm_applystatement and proof · cited by 0
- GenLoop.genLoopGenLoopEquiv_apply_coestatement · cited by 0
- Fin.continuous_appendproof · cited by 0
- IsometryEquiv.sumArrowIsometryEquivProdArrow_toHomeomorphstatement · cited by 0