Theorems · Theorem · general topology
isPathConnected_singleton
∀ {X : Type u_1} [inst : TopologicalSpace X] (x : X), IsPathConnected {x}- Defined in
- Mathlib.Topology.Connected.PathConnected
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 121 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.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- IsPathConnectedstatement · cited by 65
- JoinedIn.reflproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- isPathConnected_sphereproof · cited by 1