Theorems · Theorem · general topology
Set.Subsingleton.isClosed
∀ {X : Type u_1} [inst : TopologicalSpace X] [T1Space X] {s : Set X}, s.Subsingleton → IsClosed s- Defined in
- Mathlib.Topology.Separation.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 66 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 and proof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- IsClosedstatement · cited by 1,639
- Set.Subsingletonstatement and proof · cited by 276
- T1Spacestatement and proof · cited by 275
- isClosed_singletonproof · cited by 66
- isClosed_emptyproof · cited by 26
- Set.Subsingleton.eq_empty_or_singletonproof · cited by 16
Cited by3
Results whose statement or proof uses this declaration.
- isClosed_inter_singletonproof · cited by 1
- Set.Subsingleton.closure_eqproof · cited by 1
- isClosed_singleton_interproof · cited by 0