Theorems · Theorem · general topology
Joined.prod
∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] {x₁ x₂ : X} {y₁ y₂ : Y},
Joined x₁ x₂ → Joined y₁ y₂ → Joined (x₁, y₁) (x₂, y₂)If x₁ is joined to x₂ and y₁ is joined to y₂, then (x₁, y₁) is joined to
(x₂, y₂) in the product space.
- Defined in
- Mathlib.Topology.Connected.PathConnected
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 122 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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
- Joinedstatement and proof · cited by 29
- Joined.somePathproof · cited by 12
- Path.prodproof · cited by 9
Cited by1
Results whose statement or proof uses this declaration.
- pathComponent_prodproof · cited by 0