Theorems · Theorem · general topology
IsPathConnected.add
∀ {M : Type u_4} [inst : Add M] [inst_1 : TopologicalSpace M] [ContinuousAdd M] {s t : Set M},
IsPathConnected s → IsPathConnected t → IsPathConnected (s + t)- Defined in
- Mathlib.Topology.Connected.PathConnected
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 125 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- ContinuousAddstatement and proof · cited by 777
- Set.addstatement · cited by 338
- IsPathConnectedstatement and proof · cited by 65
- JoinedInproof · cited by 40
- Set.add_mem_addproof · cited by 30
- Set.forall_mem_image2proof · cited by 20
- JoinedIn.addproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- isPathConnected_compl_of_isPathConnected_compl_zeroproof · cited by 1