Theorems · Theorem · general topology
isPathConnected_pathComponent
∀ {X : Type u_1} [inst : TopologicalSpace X] {x : X}, IsPathConnected (pathComponent x)- Defined in
- Mathlib.Topology.Connected.PathConnected
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 127 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.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Set.mem_univproof · cited by 416
- IsPathConnectedstatement and proof · cited by 65
- pathComponentstatement · cited by 30
- isPathConnected_pathComponentInproof · cited by 6
- pathComponentIn_univproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- Pi.locallyPathConnectedSpace_iffproof · cited by 0