Theorems · Definition · order theory
Set.ordConnectedSection
{α : Type u_1} → [LinearOrder α] → Set α → Set αA set that intersects each order connected component of a set by a single point. Defined as the
range of Set.ordConnectedProj s.
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 23 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- LinearOrder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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
- LinearOrderstatement and proof · cited by 8,572
- Set.rangeproof · cited by 4,705
- Set.ordConnectedProjproof · cited by 7
Cited by8
Results whose statement or proof uses this declaration.
- Set.ordT5Nhdproof · cited by 2
- Set.compl_ordConnectedSection_ordSeparatingSet_mem_nhdsGEstatement and proof · cited by 2
- Set.dual_ordConnectedSectionstatement · cited by 1
- Set.ordConnectedSection_subsetstatement · cited by 1
- Set.compl_ordConnectedSection_ordSeparatingSet_mem_nhdsstatement and proof · cited by 1
- Set.compl_ordConnectedSection_ordSeparatingSet_mem_nhdsLEstatement and proof · cited by 1
- Set.eq_of_mem_ordConnectedSection_of_uIcc_subsetstatement and proof · cited by 1
- Set.disjoint_ordT5Nhdproof · cited by 0