Theorems · Theorem · real analysis
Complex.continuousAt_ofReal_cpow
∀ (x : ℝ) (y : ℂ), 0 < y.re ∨ x ≠ 0 → ContinuousAt (fun p => ↑p.1 ^ p.2) (x, y)
Continuity of (x, y) ↦ x ^ y as a function on ℝ × ℂ.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 206 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites38
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- Complexstatement and proof · cited by 5,565
- Set.univproof · cited by 3,945
- Real.piproof · cited by 1,774
- SProd.sprodproof · cited by 1,750
- Complex.ofRealstatement and proof · cited by 1,654
- le_of_ltproof · cited by 1,175
- Set.Iioproof · cited by 1,166
- Complex.restatement and proof · cited by 882
- Complex.Iproof · cited by 866
- ContinuousAtstatement and proof · cited by 697
- Complex.expproof · cited by 612
Cited by1
Results whose statement or proof uses this declaration.
- Complex.continuousAt_ofReal_cpow_constproof · cited by 5