Theorems · Theorem · general topology
UniformSpace.hausdorff.isClopen_singleton_empty
∀ {α : Type u_1} [inst : UniformSpace α], IsClopen {∅}- Defined in
- Mathlib.Topology.UniformSpace.Closeds
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- UniformSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
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
- nhdsproof · cited by 5,554
- Set.univproof · cited by 3,945
- UniformSpacestatement and proof · cited by 2,040
- Filter.univ_mem'proof · cited by 1,672
- IsClosedproof · cited by 1,639
- Filter.mp_memproof · cited by 1,537
- IsClopenstatement · cited by 189
- UniformSpace.ballproof · cited by 113
- Filter.univ_memproof · cited by 96
- SetRel.preimageproof · cited by 56
- SetRel.imageproof · cited by 49
Cited by2
Results whose statement or proof uses this declaration.
- UniformSpace.hausdorff.isClosedEmbedding_singletonproof · cited by 1
- TopologicalSpace.Closeds.isClopen_singleton_botproof · cited by 1