Theorems · Definition · general topology
nhdsSet
{X : Type u_1} → [TopologicalSpace X] → Set X → Filter XThe filter of neighborhoods of a set in a topological space.
- Defined in
- Mathlib.Topology.Defs.Filter
- Cited by
- 267 results in Mathlib
- Foundations
- Depth 19 from the axioms, rests on 93 definitions · uses propext, Quot.sound
- Assumes
- TopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- Set.imageproof · cited by 5,609
- nhdsproof · cited by 5,554
- SupSet.sSupproof · cited by 954
Cited by278
Results whose statement or proof uses this declaration.
- nhdsKerproof · cited by 53
- UpperHemicontinuousproof · cited by 30
- nhdsSetWithinproof · cited by 25
- UpperHemicontinuousWithinAtproof · cited by 22
- UpperHemicontinuousAtproof · cited by 21
- UpperHemicontinuousOnproof · cited by 21
- hasBasis_nhdsSetstatement · cited by 20
- nhdsSet_singletonstatement · cited by 19
- nhdsSet_monostatement · cited by 18
- IsOpen.mem_nhdsSetstatement · cited by 17
- IsCompact.elim_nhds_subcoverproof · cited by 15
- mem_nhdsSet_iff_forallstatement · cited by 12
Showing the 200 most cited of 278.