Theorems · Theorem · field theory
Polynomial.continuousOn
∀ {R : Type u_1} [inst : Semiring R] [inst_1 : TopologicalSpace R] [IsTopologicalSemiring R] (p : Polynomial R)
{s : Set R}, ContinuousOn (fun x => Polynomial.eval x p) s- Defined in
- Mathlib.Topology.Algebra.Polynomial
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Semiringstatement and proof · cited by 13,802
- Polynomialstatement and proof · cited by 5,681
- ContinuousOnstatement · cited by 1,411
- Polynomial.evalstatement · cited by 796
- IsTopologicalSemiringstatement and proof · cited by 442
- Continuous.continuousOnproof · cited by 311
- Polynomial.continuousproof · cited by 12
Cited by4
Results whose statement or proof uses this declaration.
- Polynomial.card_roots_toFinset_le_card_roots_derivative_sdiff_roots_succproof · cited by 3
- Polynomial.Chebyshev.integral_eval_T_real_mul_eval_T_real_measureTproof · cited by 2
- Polynomial.Chebyshev.integral_eq_sumZeroesproof · cited by 0
- cfc_comp_polynomialproof · cited by 0