Theorems · Theorem · general topology
IsConnected.prod
∀ {α : Type u} {β : Type v} [inst : TopologicalSpace α] [inst_1 : TopologicalSpace β] {s : Set α} {t : Set β},
IsConnected s → IsConnected t → IsConnected (s ×ˢ t)- Defined in
- Mathlib.Topology.Connected.Basic
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- SProd.sprodstatement · cited by 1,750
- IsConnectedstatement and proof · cited by 116
- Set.Nonempty.prodproof · cited by 8
- IsPreconnected.prodproof · cited by 3
Cited by5
Results whose statement or proof uses this declaration.
- AffineSubspace.isConnected_setOfPred_sSameSideproof · cited by 3
- Collinear.oangle_sign_of_sameRay_vsubproof · cited by 2
- AffineSubspace.isConnected_setOfPred_sOppSideproof · cited by 2
- AffineSubspace.isConnected_setOfPred_wOppSideproof · cited by 2
- AffineSubspace.isConnected_setOfPred_wSameSideproof · cited by 2