Theorems · Theorem · general topology
IsPreconnected.union
∀ {α : Type u} [inst : TopologicalSpace α] (x : α) {s t : Set α},
x ∈ s → x ∈ t → IsPreconnected s → IsPreconnected t → IsPreconnected (s ∪ t)- Defined in
- Mathlib.Topology.Connected.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 62 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.
Cites5
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
- IsPreconnectedstatement and proof · cited by 205
- isPreconnected_sUnionproof · cited by 3
- Set.sUnion_pairproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- IsPreconnected.prodproof · cited by 3
- IsPreconnected.union'proof · cited by 1
- IsConnected.unionproof · cited by 1