Theorems · Inductive type · general topology
TotallyDisconnectedSpace
(α : Type u) → [TopologicalSpace α] → Prop
A space is totally disconnected if all of its connected components are singletons.
- Cited by
- 295 results in Mathlib
- Foundations
- Depth 1 from the axioms, rests on 2 definitions · uses no axioms
- Assumes
- TopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement · cited by 24,529
Cited by540
Results whose statement or proof uses this declaration.
- LightProfiniteproof · cited by 90
- Profiniteproof · cited by 75
- FintypeCat.toProfinitestatement and proof · cited by 32
- FintypeCat.toLightProfinitestatement and proof · cited by 23
- ProfiniteGrp.Hom.homstatement · cited by 20
- LightProfinite.ofstatement and proof · cited by 19
- ProfiniteGrp.limitConePtAuxstatement · cited by 19
- ProfiniteAddGrp.Hom.homstatement · cited by 16
- LightProfinite.diagramstatement · cited by 13
- LightCondensed.freestatement · cited by 12
- Profinite.ofstatement and proof · cited by 11
- lightProfiniteToLightCondSetstatement · cited by 11
Showing the 200 most cited of 540.