Theorems · Theorem · general topology
ContinuousOn.snd
∀ {α : Type u_1} {β : Type u_2} {γ : Type u_3} [inst : TopologicalSpace α] [inst_1 : TopologicalSpace β]
[inst_2 : TopologicalSpace γ] {f : α → β × γ} {s : Set α}, ContinuousOn f s → ContinuousOn (fun x => (f x).2) s- Defined in
- Mathlib.Topology.ContinuousOn
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 73 from the axioms · uses propext, Classical.choice, 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
- continuous_sndproof · cited by 91
- Continuous.comp_continuousOnproof · cited by 52
Cited by5
Results whose statement or proof uses this declaration.
- Real.continuousOn_rpowIntegrand₀₁_uncurryproof · cited by 2
- Collinear.oangle_sign_of_sameRay_vsubproof · cited by 2
- MeasureTheory.continuousOn_convolution_right_with_paramproof · cited by 2
- Real.continuousOn_rpowIntegrand₁₂_uncurryproof · cited by 1
- Path.Homotopy.continuous_reflTransSymmAuxproof · cited by 0