Theorems · Definition · general topology
nhdsWithin
{X : Type u_1} → [TopologicalSpace X] → X → Set X → Filter XThe "neighborhood within" filter. Elements of 𝓝[s] x are sets containing the
intersection of s and a neighborhood of x.
- Defined in
- Mathlib.Topology.Defs.Filter
- Cited by
- 1,912 results in Mathlib
- Foundations
- Depth 48 from the axioms, rests on 538 definitions · uses propext, Quot.sound
- Assumes
- TopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- TopologicalSpacestatement and proof · cited by 24,529
- Filterstatement · cited by 8,121
- nhdsproof · cited by 5,554
- Filter.principalproof · cited by 740
Cited by1,937
Results whose statement or proof uses this declaration.
- ContinuousWithinAtproof · cited by 512
- HasFDerivWithinAtproof · cited by 356
- HasDerivWithinAtproof · cited by 333
- ContDiffWithinAtproof · cited by 283
- self_mem_nhdsWithinstatement · cited by 215
- nhdsWithin_le_nhdsstatement and proof · cited by 145
- nhdsWithin_univstatement · cited by 88
- Filter.codiscreteWithinproof · cited by 87
- TendstoLocallyUniformlyOnproof · cited by 84
- nhdsWithin_monostatement · cited by 82
- MeasureTheory.LocallyIntegrableOnproof · cited by 81
- AccPtproof · cited by 75
Showing the 200 most cited of 1,937.