Theorems · Theorem · Lie groups
Continuous.const_mul
∀ {M : Type u_1} [inst : TopologicalSpace M] [inst_1 : Mul M] [SeparatelyContinuousMul M] {X : Type u_2}
[inst_3 : TopologicalSpace X] {f : X → M}, Continuous f → ∀ (b : M), Continuous fun x => b * f x- Defined in
- Mathlib.Topology.Algebra.Monoid.Defs
- Cited by
- 27 results in Mathlib
- Foundations
- Depth 8 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- Continuousstatement and proof · cited by 2,592
- Continuous.compproof · cited by 371
- SeparatelyContinuousMulstatement and proof · cited by 133
- continuous_const_mulproof · cited by 47
Cited by27
Results whose statement or proof uses this declaration.
- compact_covered_by_mul_left_translatesproof · cited by 4
- integrableOn_exp_mul_complex_Ioiproof · cited by 4
- Complex.tsum_exp_neg_quadraticproof · cited by 3
- continuousAt_of_locally_lipschitzproof · cited by 3
- IsSemitopologicalSemiring.continuousNeg_of_mulproof · cited by 3
- mulLeft_continuousproof · cited by 2
- summableLocallyUniformlyOn_iteratedDerivWithin_smul_cexpproof · cited by 2
- continuousAt_jacobiTheta₂'proof · cited by 2
- Path.trans_continuous_familyproof · cited by 1
- DirichletCharacter.LFunction_changeLevelproof · cited by 1
- LipschitzWith.completion_extensionproof · cited by 1
- GaussianFourier.integral_cexp_neg_mul_sq_add_real_mul_Iproof · cited by 1