Theorems · Theorem · field theory
Polynomial.continuous_aeval
∀ {R : Type u_1} {A : Type u_2} [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : Algebra R A]
[inst_3 : TopologicalSpace A] [IsTopologicalSemiring A] (p : Polynomial R), Continuous fun x => (Polynomial.aeval x) p- Defined in
- Mathlib.Topology.Algebra.Polynomial
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 110 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- TopologicalSpacestatement and proof · cited by 24,529
- Semiringstatement and proof · cited by 13,802
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- Polynomialstatement and proof · cited by 5,681
- AlgHomstatement · cited by 3,236
- Continuousstatement · cited by 2,592
- RingHomClass.toRingHomproof · cited by 746
- Polynomial.aevalstatement · cited by 615
- IsTopologicalSemiringstatement and proof · cited by 442
- Algebra.ofIdproof · cited by 166
Cited by6
Results whose statement or proof uses this declaration.
- continuous_bernoulliFunproof · cited by 3
- Liouville.exists_pos_real_of_irrational_rootproof · cited by 1
- Polynomial.C_eq_or_isOpenQuotientMap_evalproof · cited by 1
- Polynomial.continuousAt_aevalproof · cited by 0
- Polynomial.continuousOn_aevalproof · cited by 0
- Polynomial.continuousWithinAt_aevalproof · cited by 0