Theorems · Theorem · general topology
TopologicalSpace.Compacts.isPreconnected_Ioc
∀ {α : Type u_1} [inst : TopologicalSpace α] {K L : TopologicalSpace.Compacts α},
IsPreconnected ↑L → IsPreconnected (Set.Ioc K L)- Defined in
- Mathlib.Topology.Sets.VietorisTopology
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 95 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.
Cites12
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
- SetLike.coestatement and proof · cited by 8,199
- Set.Iccproof · cited by 1,702
- Set.Iocstatement and proof · cited by 971
- TopologicalSpace.Compactsstatement and proof · cited by 386
- IsPreconnectedstatement and proof · cited by 205
- Set.left_mem_Iccproof · cited by 67
- Set.right_mem_Iccproof · cited by 60
- ne_bot_of_gtproof · cited by 18
- Set.Icc_subset_Ioc_leftproof · cited by 4
- isPreconnected_of_forallproof · cited by 3
- TopologicalSpace.Compacts.isPreconnected_Iccproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- TopologicalSpace.NonemptyCompacts.isPreconnected_Iocproof · cited by 0