Theorems · Theorem · general topology
TopologicalSpace.nhds_generateFrom
∀ {α : Type u} {g : Set (Set α)} {a : α}, nhds a = ⨅ s ∈ {s | a ∈ s ∧ s ∈ g}, Filter.principal s- Defined in
- Mathlib.Topology.Order
- Cited by
- 15 results in Mathlib
- Foundations
- Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites25
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- TopologicalSpaceproof · cited by 24,529
- Filterstatement and proof · cited by 8,121
- Set.ofPredstatement and proof · cited by 6,101
- nhdsstatement · cited by 5,554
- Set.univproof · cited by 3,945
- LE.le.transproof · cited by 3,151
- IsOpenproof · cited by 2,400
- le_antisymmproof · cited by 2,068
- iInfstatement and proof · cited by 1,690
- Filter.principalstatement and proof · cited by 740
- le_topproof · cited by 411
Cited by15
Results whose statement or proof uses this declaration.
- TopologicalSpace.IsTopologicalBasis.mem_nhds_iffproof · cited by 13
- nhds_eq_orderproof · cited by 9
- TopologicalSpace.IsTopologicalBasis.of_hasBasis_nhdsproof · cited by 6
- Filter.nhds_eqproof · cited by 6
- ContinuousMap.nhds_compactOpenproof · cited by 4
- ultrafilter_converges_iffproof · cited by 4
- isCompact_generateFromproof · cited by 2
- TopCat.Presheaf.EtaleSpace.eventually_nhdsproof · cited by 2
- ultrafilter_comap_pure_nhdsproof · cited by 2
- nhds_falseproof · cited by 1
- continuousOn_to_generateFrom_iffproof · cited by 1
- ContinuousMap.compactOpen_eq_generateFromproof · cited by 1