Theorems · Theorem · special functions
Continuous.cexp
∀ {α : Type u_1} [inst : TopologicalSpace α] {f : α → ℂ}, Continuous f → Continuous fun y => Complex.exp (f y)- Defined in
- Mathlib.Analysis.SpecialFunctions.Exp
- Cited by
- 37 results in Mathlib
- Foundations
- Depth 159 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- Complexstatement and proof · cited by 5,565
- Continuousstatement and proof · cited by 2,592
- Complex.expstatement · cited by 612
- Continuous.continuousAtproof · cited by 297
- continuous_iff_continuousAtproof · cited by 139
- ContinuousAt.cexpproof · cited by 4
Cited by37
Results whose statement or proof uses this declaration.
- Real.continuous_expproof · cited by 14
- Complex.continuous_cosproof · cited by 7
- Complex.continuous_sinproof · cited by 5
- integrableOn_exp_mul_complex_Ioiproof · cited by 4
- Complex.tsum_exp_neg_quadraticproof · cited by 3
- ProbabilityTheory.complexMGF_id_mapproof · cited by 3
- ProbabilityTheory.hasDerivAt_integral_pow_mul_expproof · cited by 3
- PhragmenLindelof.horizontal_stripproof · cited by 3
- MeasureTheory.charFun_convproof · cited by 2
- MeasureTheory.charFun_map_smulproof · cited by 2
- Real.circleMap.continuousproof · cited by 2
- Complex.continuous_coshproof · cited by 2