Theorems · Theorem · general topology
ContinuousOn.fun_const_smul
∀ {M : Type u_1} {α : Type u_2} {β : Type u_3} [inst : TopologicalSpace α] [inst_1 : SMul M α] [ContinuousConstSMul M α]
[inst_3 : TopologicalSpace β] {g : β → α} {s : Set β}, ContinuousOn g s → ∀ (c : M), ContinuousOn (fun i => c • g i) sEta-expanded form of ContinuousOn.const_smul
- Defined in
- Mathlib.Topology.Algebra.ConstMulAction
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 62 from the axioms · uses propext, Quot.sound
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.
- Setstatement · cited by 53,352
- TopologicalSpacestatement · cited by 24,529
- ContinuousOnstatement · cited by 1,411
- ContinuousConstSMulstatement · cited by 832
- ContinuousOn.const_smulproof · cited by 5
Cited by10
Results whose statement or proof uses this declaration.
- cfcₙ_smulproof · cited by 5
- cfc_smulproof · cited by 4
- selfAdjoint.norm_sq_expUnitary_sub_oneproof · cited by 3
- cfc_comp_smulproof · cited by 3
- cfcₙ_comp_smulproof · cited by 2
- expUnitary_argSelfAdjointproof · cited by 2
- CStarAlgebra.convexOn_ringInverseproof · cited by 1
- CFC.cfcₙ_rpowIntegrand₀₁_eq_cfcₙ_rpowIntegrand₀₁_oneproof · cited by 1
- CFC.log_smulproof · cited by 0
- argSelfAdjoint_expUnitaryproof · cited by 0