Theorems · Theorem · general topology
connectedComponent_eq_iff_joined
∀ {X : Type u_1} [inst : TopologicalSpace X] [LocallyPathConnectedSpace X] (x y : X),
connectedComponent x = connectedComponent y ↔ Joined x y- Cited by
- 1 results in Mathlib
- Foundations
- Depth 133 from the axioms · uses propext, Classical.choice, Quot.sound
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
- connectedComponentstatement and proof · cited by 68
- LocallyPathConnectedSpacestatement and proof · cited by 53
- Joinedstatement · cited by 29
- mem_pathComponent_iffproof · cited by 2
- pathComponent_eq_connectedComponentproof · cited by 2
- connectedComponent_eq_iff_memproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- connectedComponentSetoid_eq_pathSetoidproof · cited by 0