Theorems · Theorem · general topology
Continuous.prodMap
∀ {X : Type u} {Y : Type v} {W : Type u_1} {Z : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y]
[inst_2 : TopologicalSpace Z] [inst_3 : TopologicalSpace W] {f : Z → X} {g : W → Y},
Continuous f → Continuous g → Continuous (Prod.map f g)- Defined in
- Mathlib.Topology.Constructions.SumProd
- Cited by
- 28 results in Mathlib
- Foundations
- Depth 74 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 and proof · cited by 2,592
- Continuous.prodMkproof · cited by 127
- Continuous.fst'proof · cited by 4
- Continuous.snd'proof · cited by 3
Cited by28
Results whose statement or proof uses this declaration.
- IsProperMap.prodMapproof · cited by 7
- CompactSpace.uniformContinuous_of_continuousproof · cited by 5
- IsOpenQuotientMap.prodMapproof · cited by 4
- continuous_sInf_dom₂proof · cited by 4
- ContinuousMap.continuous_uncurry_of_continuousproof · cited by 3
- IsEvenlyCovered.of_trivializationproof · cited by 2
- Path.trans_continuous_familyproof · cited by 1
- Path.continuous_uncurry_extend_of_continuous_familyproof · cited by 1
- ContinuousMap.continuousOn_mkD_of_uncurryproof · cited by 1
- ContinuousMap.continuousOn_mkD_restrict_of_uncurryproof · cited by 1
- ContinuousMap.continuous_mkD_restrict_of_uncurryproof · cited by 1
- RestrictedProduct.continuous_dom_prod_leftproof · cited by 1