Theorems · Theorem · general topology
R0Space.closure_singleton
∀ {X : Type u_1} [inst : TopologicalSpace X] [R0Space X] (x : X), closure {x} = (nhds x).ker- Defined in
- Mathlib.Topology.Separation.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpaceR0Space
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- Set.extproof · cited by 2,266
- closurestatement · cited by 1,254
- Specializesproof · cited by 176
- Filter.kerstatement · cited by 40
- R0Spacestatement and proof · cited by 22
- ker_nhds_eq_specializesproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- GroupFilterBasis.t2Space_iffproof · cited by 1
- AddGroupFilterBasis.t2Space_iffproof · cited by 1