Theorems · Theorem · general topology
Set.Subsingleton.closure_eq
∀ {X : Type u_1} [inst : TopologicalSpace X] [T1Space X] {s : Set X}, s.Subsingleton → closure s = s- Defined in
- Mathlib.Topology.Separation.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 67 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.
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
- closurestatement · cited by 1,254
- Set.Subsingletonstatement and proof · cited by 276
- T1Spacestatement and proof · cited by 275
- IsClosed.closure_eqproof · cited by 139
- Set.Subsingleton.isClosedproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- Set.Subsingleton.closureproof · cited by 2