Theorems · Theorem · field theory
Polynomial.continuous
∀ {R : Type u_1} [inst : Semiring R] [inst_1 : TopologicalSpace R] [IsTopologicalSemiring R] (p : Polynomial R),
Continuous fun x => Polynomial.eval x p- Defined in
- Mathlib.Topology.Algebra.Polynomial
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- RingHom.idproof · cited by 18,349
- Semiringstatement and proof · cited by 13,802
- Polynomialstatement and proof · cited by 5,681
- Continuousstatement · cited by 2,592
- Polynomial.evalstatement · cited by 796
- IsTopologicalSemiringstatement and proof · cited by 442
- Polynomial.continuous_eval₂proof · cited by 2
Cited by12
Results whose statement or proof uses this declaration.
- Polynomial.continuousOnproof · cited by 4
- Polynomial.zero_lt_eval_of_roots_lt_of_leadingCoeff_nonnegproof · cited by 3
- bernoulliFourierCoeff_recurrenceproof · cited by 2
- periodizedBernoulli.continuousproof · cited by 1
- cfc_map_polynomialproof · cited by 1
- Polynomial.continuousAtproof · cited by 1
- PadicInt.continuous_multichooseproof · cited by 1
- Polynomial.mahlerMeasure_le_sqrt_sum_sq_norm_coeffproof · cited by 1
- Polynomial.isProperMap_evalproof · cited by 1
- Polynomial.exists_forall_norm_leproof · cited by 0
- Polynomial.continuousWithinAtproof · cited by 0
- LindemannWeierstrass.integral_exp_mul_evalproof · cited by 0