Theorems · Definition · general topology
IsTotallySeparated
{α : Type u} → [TopologicalSpace α] → Set α → PropA set s is called totally separated if any two points of this set can be separated
by two disjoint open sets covering s.
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- IsOpenproof · cited by 2,400
- Disjointproof · cited by 2,201
- Set.Pairwiseproof · cited by 321
Cited by9
Results whose statement or proof uses this declaration.
- TotallySeparatedSpace.casesOnstatement and proof · cited by 1
- totallySeparatedSpace_iffstatement and proof · cited by 1
- isTotallyDisconnected_of_isTotallySeparatedstatement and proof · cited by 1
- TotallySeparatedSpace.isTotallySeparated_univstatement · cited by 0
- TotallySeparatedSpace.recOnstatement and proof · cited by 0
- krullTopology_isTotallySeparatedstatement · cited by 0
- IsTotallySeparated.isTotallyDisconnectedstatement · cited by 0
- isTotallySeparated_emptystatement · cited by 0
- isTotallySeparated_singletonstatement · cited by 0