Theorems · Theorem · general topology
isTotallyDisconnected_of_isTotallySeparated
∀ {α : Type u} [inst : TopologicalSpace α] {s : Set α}, IsTotallySeparated s → IsTotallyDisconnected s- Cited by
- 1 results in Mathlib
- Foundations
- Depth 61 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.
Cites11
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
- LE.le.transproof · cited by 3,151
- IsOpenproof · cited by 2,400
- Disjointproof · cited by 2,201
- IsPreconnectedproof · cited by 205
- Set.Nonempty.ne_emptyproof · cited by 65
- Set.inter_emptyproof · cited by 36
- Disjoint.inter_eqproof · cited by 18
- IsTotallyDisconnectedstatement · cited by 14
- IsTotallySeparatedstatement and proof · cited by 7
Cited by1
Results whose statement or proof uses this declaration.
- IsTotallySeparated.isTotallyDisconnectedproof · cited by 0