Theorems · Theorem · general topology
nhdsKer_singleton_eq_ker_nhds
∀ {X : Type u_2} [inst : TopologicalSpace X] (x : X), nhdsKer {x} = (nhds x).ker- Defined in
- Mathlib.Topology.NhdsKer
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 52 from the axioms · uses propext, Classical.choice, 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 · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- nhdsstatement and proof · cited by 5,554
- nhdsKerstatement · cited by 53
- Filter.kerstatement and proof · cited by 40
- nhdsSet_singletonproof · cited by 19
Cited by3
Results whose statement or proof uses this declaration.
- nhdsKer_pairproof · cited by 1
- nhdsKer_singleton_piproof · cited by 1
- mem_nhdsKer_singletonproof · cited by 0