Theorems · Theorem · general topology
PathConnectedSpace.nonempty
∀ {X : Type u_4} {inst : TopologicalSpace X} [self : PathConnectedSpace X], Nonempty XA path-connected space must be nonempty.
- Defined in
- Mathlib.Topology.Connected.PathConnected
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 2 from the axioms · uses no axioms
- Assumes
- PathConnectedSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement and proof · cited by 24,529
- PathConnectedSpacestatement and proof · cited by 26
Cited by1
Results whose statement or proof uses this declaration.
- pathConnectedSpace_iff_zerothHomotopyproof · cited by 0