Theorems · Theorem · general topology
ContinuousAt.prodMk
∀ {X : Type u} {Y : Type v} {Z : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y]
[inst_2 : TopologicalSpace Z] {f : X → Y} {g : X → Z} {x : X},
ContinuousAt f x → ContinuousAt g x → ContinuousAt (fun x => (f x, g x)) x- Defined in
- Mathlib.Topology.Constructions.SumProd
- Cited by
- 18 results in Mathlib
- Foundations
- Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
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
- ContinuousAtstatement and proof · cited by 697
- Filter.Tendsto.prodMk_nhdsproof · cited by 46
Cited by18
Results whose statement or proof uses this declaration.
- ContinuousAt.prodMapproof · cited by 5
- ContinuousAt.comp₂proof · cited by 3
- continuousAt_cpow_constproof · cited by 3
- Complex.continuousAt_cpow_const_of_re_posproof · cited by 2
- EuclideanGeometry.continuousAt_oangleproof · cited by 2
- ContinuousAt.comp_div_casesproof · cited by 1
- Bundle.Trivialization.continuousAt_symm_prodMk_leftproof · cited by 1
- Complex.continuousAt_ofReal_cpowproof · cited by 1
- NNReal.continuousAt_rpowproof · cited by 1
- ContinuousAt.IccExtendproof · cited by 1
- ContinuousAt.clm_compproof · cited by 1
- FiberBundleCore.continuous_const_sectionproof · cited by 0