Theorems · Definition · algebraic topology
LoopSpace
(X : Type u_2) → [TopologicalSpace X] → X → Type u_2
The space of paths with both endpoints equal to a specified point x : X.
Denoted as Ω, within the Topology.Homotopy namespace.
- Defined in
- Mathlib.Topology.Homotopy.HomotopyGroup
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 2 from the axioms · uses no axioms
- Assumes
- TopologicalSpace
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
- Pathproof · cited by 318
Cited by13
Results whose statement or proof uses this declaration.
- GenLoop.toLoopstatement · cited by 12
- GenLoop.fromLoopstatement and proof · cited by 8
- GenLoop.loopHomeostatement · cited by 5
- GenLoop.loopHomeo_applystatement · cited by 1
- GenLoop.loopHomeo_symm_applystatement and proof · cited by 1
- GenLoop.toLoop_applystatement · cited by 1
- genLoopEquivOfUniquestatement and proof · cited by 1
- GenLoop.to_fromstatement and proof · cited by 0
- HomotopyGroup.genLoopEquivOfUnique_transAtstatement and proof · cited by 0
- GenLoop.continuous_fromLoopstatement · cited by 0
- GenLoop.continuous_toLoopstatement · cited by 0
- GenLoop.fromLoop_applystatement and proof · cited by 0