Theorems · Theorem · complex analysis
Complex.continuous_circleTransform
∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℂ E] {R : ℝ},
0 < R →
∀ {f : ℂ → E} {z w : ℂ},
ContinuousOn f (Metric.sphere z R) → w ∈ Metric.ball z R → Continuous (Complex.circleTransform R z w f)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 190 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Realstatement and proof · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- Complexstatement and proof · cited by 5,565
- Continuousstatement and proof · cited by 2,592
- LT.lt.leproof · cited by 2,189
- ContinuousOnstatement and proof · cited by 1,411
- Complex.Iproof · cited by 866
- Metric.ballstatement and proof · cited by 735
- Metric.spherestatement and proof · cited by 371
- continuous_constproof · cited by 278
Cited by1
Results whose statement or proof uses this declaration.
- Complex.continuous_circleTransformDerivproof · cited by 0