Theorems · Theorem · general topology
ker_nhds
∀ {X : Type u_1} [inst : TopologicalSpace X] [T1Space X] (x : X), (nhds x).ker = {x}- Defined in
- Mathlib.Topology.Separation.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpaceT1Space
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- Set.ofPredproof · cited by 6,101
- nhdsstatement · cited by 5,554
- T1Spacestatement and proof · cited by 275
- Filter.kerstatement · cited by 40
- ker_nhds_eq_specializesproof · cited by 3
- specializes_eq_eqproof · cited by 2
Cited by4
Results whose statement or proof uses this declaration.
- Summable.countable_supportproof · cited by 2
- biInter_basis_nhdsproof · cited by 2
- Circle.eq_one_of_forall_pow_mem_centeredArc_pi_div_twoproof · cited by 0
- Multipliable.countable_mulSupportproof · cited by 0