Theorems · Theorem · general topology
IsPathConnected.nonempty
∀ {X : Type u_1} [inst : TopologicalSpace X] {F : Set X}, IsPathConnected F → F.Nonempty- Defined in
- Mathlib.Topology.Connected.PathConnected
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 129 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
- Set.Nonemptystatement · cited by 2,627
- IsPathConnectedstatement and proof · cited by 65
- isPathConnected_iffproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- IsSimplyConnected.nonemptyproof · cited by 1
- IsPathConnected.prodproof · cited by 0