Theorems · Theorem · general topology
disjoint_nhds_atTop_iff
∀ {α : Type u} [inst : TopologicalSpace α] [inst_1 : Preorder α] [ClosedIciTopology α] {a : α},
Disjoint (nhds a) Filter.atTop ↔ ¬IsTop a- Defined in
- Mathlib.Topology.Order.OrderClosed
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
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 and proof · cited by 8,121
- Preorderstatement and proof · cited by 7,952
- nhdsstatement and proof · cited by 5,554
- Filter.atTopstatement and proof · cited by 2,405
- Disjointstatement and proof · cited by 2,201
- le_rflproof · cited by 1,558
- IsOpen.mem_nhdsproof · cited by 470
- ClosedIciTopologystatement and proof · cited by 156
- mem_of_mem_nhdsproof · cited by 126
- IsClosed.isOpen_complproof · cited by 126
- IsTopstatement and proof · cited by 77
Cited by1
Results whose statement or proof uses this declaration.
- disjoint_nhds_atTopproof · cited by 4