Theorems · Theorem · general topology
IsConnected.union
∀ {α : Type u} [inst : TopologicalSpace α] {s t : Set α},
(s ∩ t).Nonempty → IsConnected s → IsConnected t → IsConnected (s ∪ t)- Defined in
- Mathlib.Topology.Connected.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- Set.Nonemptystatement and proof · cited by 2,627
- IsConnectedstatement and proof · cited by 116
- IsConnected.isPreconnectedproof · cited by 36
- Set.mem_union_leftproof · cited by 32
- Set.mem_of_mem_inter_rightproof · cited by 13
- Set.mem_of_mem_inter_leftproof · cited by 10
- IsPreconnected.unionproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- IsSelfAdjoint.isConnected_spectrum_complproof · cited by 1