Theorems · Theorem · general topology
continuous_sumMap
∀ {X : Type u} {Y : Type v} {W : Type u_1} {Z : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y]
[inst_2 : TopologicalSpace W] [inst_3 : TopologicalSpace Z] {f : X → Y} {g : Z → W},
Continuous (Sum.map f g) ↔ Continuous f ∧ Continuous g- Defined in
- Mathlib.Topology.Constructions.SumProd
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- Iff.andproof · cited by 33
- Topology.IsEmbedding.continuous_iffproof · cited by 21
- Topology.IsEmbedding.inlproof · cited by 5
- Topology.IsEmbedding.inrproof · cited by 5
- continuous_sumElimproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- Continuous.sumMapproof · cited by 1