Theorems · Theorem · general topology
CofiniteTopology.nhds_eq
∀ {X : Type u} (x : CofiniteTopology X), nhds x = pure x ⊔ Filter.cofinite- Defined in
- Mathlib.Topology.Constructions
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 83 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.
- Setproof · cited by 53,352
- Filterstatement · cited by 8,121
- nhdsstatement · cited by 5,554
- Compl.complproof · cited by 2,925
- Set.Nonemptyproof · cited by 2,627
- Set.Finiteproof · cited by 1,814
- Filter.mem_of_supersetproof · cited by 308
- Set.Subset.rflproof · cited by 255
- Filter.cofinitestatement and proof · cited by 251
- Filter.extproof · cited by 60
- CofiniteTopologystatement and proof · cited by 10
- TopologicalSpace.cofinitestatement · cited by 9
Cited by2
Results whose statement or proof uses this declaration.
- OnePoint.not_continuous_cofiniteTopology_of_symmproof · cited by 1
- CofiniteTopology.mem_nhds_iffproof · cited by 0