Theorems · Theorem · general topology
SuccOrder.nhdsLT_eq_nhdsNE
∀ {α : Type u} [inst : TopologicalSpace α] [inst_1 : LinearOrder α] [ClosedIciTopology α] [SuccOrder α] (a : α),
nhdsWithin a (Set.Iio a) = nhdsWithin a {a}ᶜ- Defined in
- Mathlib.Topology.Order.OrderClosed
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- Setstatement · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- LinearOrderstatement and proof · cited by 8,572
- Filterstatement and proof · cited by 8,121
- Compl.complstatement · cited by 2,925
- nhdsWithinstatement and proof · cited by 1,912
- Set.Iiostatement and proof · cited by 1,166
- SuccOrderstatement and proof · cited by 574
- ClosedIciTopologystatement and proof · cited by 156
- bot_sup_eqproof · cited by 32
- SuccOrder.nhdsGTproof · cited by 5
- nhdsGT_sup_nhdsLTproof · cited by 1
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.