Theorems · Theorem · general topology
TopologicalSpace.Compacts.isPreconnected_Icc
∀ {α : Type u_1} [inst : TopologicalSpace α] {K L : TopologicalSpace.Compacts α},
K ≠ ⊥ → IsPreconnected ↑L → IsPreconnected (Set.Icc K L)- Defined in
- Mathlib.Topology.Sets.VietorisTopology
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 94 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.
Cites25
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- SetLike.coestatement and proof · cited by 8,199
- Set.ofPredproof · cited by 6,101
- Set.imageproof · cited by 5,609
- Set.preimageproof · cited by 4,946
- Bot.botstatement and proof · cited by 4,720
- Set.Nonemptyproof · cited by 2,627
- Set.Iccstatement and proof · cited by 1,702
- TopologicalSpace.Compactsstatement and proof · cited by 386
- le_sup_leftproof · cited by 265
- IsPreconnectedstatement and proof · cited by 205
Cited by2
Results whose statement or proof uses this declaration.
- TopologicalSpace.Compacts.isPreconnected_Iocproof · cited by 1
- TopologicalSpace.NonemptyCompacts.isPreconnected_Iccproof · cited by 0