Theorems · Theorem · general topology
pathComponentIn_univ
∀ {X : Type u_1} [inst : TopologicalSpace X] (x : X), pathComponentIn Set.univ x = pathComponent x- Defined in
- Mathlib.Topology.Connected.PathConnected
- Cited by
- 3 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.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setstatement · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Set.Elemproof · cited by 7,166
- Set.ofPredproof · cited by 6,101
- Set.univstatement · cited by 3,945
- unitIntervalproof · cited by 607
- Pathproof · cited by 318
- pathComponentstatement · cited by 30
- pathComponentInstatement · cited by 19
Cited by3
Results whose statement or proof uses this declaration.
- IsOpen.pathComponentproof · cited by 2
- isPathConnected_pathComponentproof · cited by 1
- pathConnectedSpace_iff_eqproof · cited by 0