Theorems · Theorem · general topology
ker_nhds_eq_specializes
∀ {X : Type u_1} [inst : TopologicalSpace X] {x : X}, (nhds x).ker = {y | y ⤳ x}- Defined in
- Mathlib.Topology.Inseparable
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 77 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.
Cites7
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
- Set.ofPredstatement and proof · cited by 6,101
- nhdsstatement and proof · cited by 5,554
- Set.extproof · cited by 2,266
- Specializesstatement · cited by 176
- Filter.kerstatement · cited by 40
Cited by3
Results whose statement or proof uses this declaration.
- ker_nhdsproof · cited by 4
- R0Space.closure_singletonproof · cited by 2
- mem_nhdsKer_singletonproof · cited by 0