Theorems · Theorem · general topology
SuccOrder.nhdsGT
∀ {α : Type u} [inst : TopologicalSpace α] [inst_1 : LinearOrder α] [ClosedIciTopology α] {a : α} [SuccOrder α],
nhdsWithin a (Set.Ioi a) = ⊥- Defined in
- Mathlib.Topology.Order.OrderClosed
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- LinearOrderstatement and proof · cited by 8,572
- Filterstatement · cited by 8,121
- Bot.botstatement and proof · cited by 4,720
- nhdsWithinstatement and proof · cited by 1,912
- Set.Ioistatement · cited by 1,463
- SuccOrderstatement and proof · cited by 574
- IsMaxproof · cited by 372
- ClosedIciTopologystatement and proof · cited by 156
- nhdsWithin_emptyproof · cited by 16
- Order.covBy_succ_of_not_isMaxproof · cited by 8
- IsMax.Ioi_eqproof · cited by 6
Cited by5
Results whose statement or proof uses this declaration.
- SuccOrder.nhdsLE_eq_nhdsproof · cited by 2
- DiscreteTopology.of_predOrder_succOrderproof · cited by 1
- SuccOrder.nhdsLT_eq_nhdsNEproof · cited by 0
- MeasureTheory.Filtration.rightCont_eq_selfproof · cited by 0
- SuccOrder.nhdsGEproof · cited by 0