Theorems · Theorem · general topology
continuous_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}, (Continuous fun x => (f x, g x)) ↔ Continuous f ∧ Continuous g- Defined in
- Mathlib.Topology.Constructions.SumProd
- Cited by
- 5 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.
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 · cited by 2,592
- continuous_induced_rngproof · cited by 38
- Iff.andproof · cited by 33
- continuous_inf_rngproof · cited by 1
Cited by5
Results whose statement or proof uses this declaration.
- Continuous.prodMkproof · cited by 127
- continuous_fstproof · cited by 103
- continuous_sndproof · cited by 91
- AddUnits.continuous_iffproof · cited by 3
- Continuous.of_coeHom_compproof · cited by 1