Theorems · Definition · general topology
CommRingCat.HomTopology.mvPolynomialHomeomorph
(σ : Type v) →
(R A : CommRingCat) →
[inst : TopologicalSpace ↑R] →
[IsTopologicalRing ↑R] → (CommRingCat.of (MvPolynomial σ ↑A) ⟶ R) ≃ₜ (A ⟶ R) × (σ → ↑R)Hom(A[Xᵢ], R) is homeomorphic to Hom(A, R) × Rⁱ.
- Defined in
- Mathlib.Algebra.Category.Ring.Topology
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 96 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Quiver.Homstatement and proof · cited by 32,603
- TopologicalSpacestatement and proof · cited by 24,529
- CategoryTheory.CategoryStruct.compproof · cited by 17,999
- Finsuppstatement · cited by 5,255
- CategoryTheory.ConcreteCategory.homproof · cited by 4,022
- CommRingCatstatement and proof · cited by 2,333
- MvPolynomialstatement and proof · cited by 2,140
- CommRingCat.carrierstatement and proof · cited by 1,096
- Homeomorphstatement · cited by 725
- MvPolynomial.Xproof · cited by 552
- CommRingCat.Hom.homproof · cited by 432
Cited by6
Results whose statement or proof uses this declaration.
- CommRingCat.HomTopology.mvPolynomialHomeomorph_apply_sndstatement and proof · cited by 2
- CommRingCat.HomTopology.mvPolynomialHomeomorph_apply_fststatement and proof · cited by 1
- CommRingCat.HomTopology.mvPolynomialHomeomorph_symm_apply_homstatement and proof · cited by 1
- CommRingCat.HomTopology.isClosedEmbedding_homproof · cited by 0
- CommRingCat.HomTopology.isEmbedding_pushoutproof · cited by 0
- CommRingCat.HomTopology.mvPolynomialHomeomorph.congr_simpstatement and proof · cited by 0