Theorems · Theorem · general topology
nhdsNE_le_cofinite
∀ {α : Type u_3} [inst : TopologicalSpace α] [T1Space α] (a : α), nhdsWithin a {a}ᶜ ≤ Filter.cofinite- Defined in
- Mathlib.Topology.Separation.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpaceT1Space
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- Filterstatement · cited by 8,121
- Compl.complstatement · cited by 2,925
- nhdsWithinstatement · cited by 1,912
- eq_or_neproof · cited by 1,117
- T1Spacestatement and proof · cited by 275
- Filter.cofinitestatement · cited by 251
- self_mem_nhdsWithinproof · cited by 215
- Filter.le_cofinite_iff_compl_singleton_memproof · cited by 4
- eventually_ne_nhdsWithinproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- Function.update_eventuallyEq_nhdsNEproof · cited by 1