Theorems · Theorem · general topology
ContinuousOn.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 (c • g) s- Defined in
- Mathlib.Topology.Algebra.ConstMulAction
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 61 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 and proof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- ContinuousOnstatement and proof · cited by 1,411
- ContinuousConstSMulstatement and proof · cited by 832
- ContinuousWithinAt.const_smulproof · cited by 3
Cited by5
Results whose statement or proof uses this declaration.
- ContinuousOn.fun_const_smulproof · cited by 10
- Complex.integral_boundary_rect_of_hasFDerivAt_real_off_countableproof · cited by 3
- intervalIntegral.integral_unitInterval_deriv_eq_subproof · cited by 2
- InnerProductSpace.HarmonicContOnCl.const_smulproof · cited by 1
- DiffContOnCl.const_smulproof · cited by 0