Theorems · Theorem · general topology
Polynomial.toContinuousMapOnAlgHom_apply
∀ {R : Type u_1} [inst : CommSemiring R] [inst_1 : TopologicalSpace R] [inst_2 : IsTopologicalSemiring R] (X : Set R)
(p : Polynomial R), (Polynomial.toContinuousMapOnAlgHom X) p = p.toContinuousMapOn X- Cited by
- 5 results in Mathlib
- Foundations
- Depth 107 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement and proof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- CommSemiringstatement and proof · cited by 10,911
- Set.Elemstatement · cited by 7,166
- Polynomialstatement and proof · cited by 5,681
- AlgHomstatement · cited by 3,236
- ContinuousMapstatement · cited by 2,491
- IsTopologicalSemiringstatement and proof · cited by 442
- Polynomial.toContinuousMapOnAlgHomstatement and proof · cited by 14
- Polynomial.toContinuousMapOnstatement · cited by 9
Cited by5
Results whose statement or proof uses this declaration.
- ContinuousMap.comp_attachBound_mem_closureproof · cited by 1
- polynomialFunctions_closure_eq_top'proof · cited by 1
- polynomialFunctions_coeproof · cited by 1
- ContinuousMap.induction_onproof · cited by 1
- ContinuousMap.ker_evalStarAlgHom_eq_closure_adjoin_idproof · cited by 1