Theorems · Theorem · general topology
disjoint_nhds_atTop
∀ {α : Type u} [inst : Preorder α] [NoTopOrder α] [inst_2 : TopologicalSpace α] [ClosedIciTopology α] (a : α),
Disjoint (nhds a) Filter.atTop- Defined in
- Mathlib.Topology.Order.OrderClosed
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- Filterstatement · cited by 8,121
- Preorderstatement and proof · cited by 7,952
- nhdsstatement · cited by 5,554
- Filter.atTopstatement · cited by 2,405
- Disjointstatement · cited by 2,201
- ClosedIciTopologystatement and proof · cited by 156
- NoTopOrderstatement and proof · cited by 50
- not_isTopproof · cited by 5
- disjoint_nhds_atTop_iffproof · cited by 1
Cited by4
Results whose statement or proof uses this declaration.
- not_tendsto_atTop_of_tendsto_nhdsproof · cited by 9
- not_tendsto_nhds_of_tendsto_atTopproof · cited by 7
- summable_jacobiTheta₂_term_iffproof · cited by 4
- nhds_inf_atTopproof · cited by 1