Theorems · Inductive type · algebraic topology
SimplyConnectedSpace
(X : Type u_3) → [TopologicalSpace X] → Prop
A simply connected space is one whose fundamental groupoid is equivalent to Discrete Unit
- Cited by
- 19 results in Mathlib
- Foundations
- Depth 1 from the axioms · uses no axioms
- Assumes
- TopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement · cited by 24,529
Cited by24
Results whose statement or proof uses this declaration.
- IsSimplyConnectedproof · cited by 13
- IsQuotientCoveringMap.monodromyPerm_injectivestatement and proof · cited by 2
- IsSimplyConnected.simplyConnectedSpacestatement · cited by 2
- simply_connected_iff_loops_nullhomotopicstatement · cited by 1
- IsSimplyConnected.isPathConnectedproof · cited by 1
- IsQuotientCoveringMap.fundamentalGroupToMulOpposite_injectivestatement and proof · cited by 1
- Complex.exists_continuousOn_eqOn_exp_compproof · cited by 1
- IsCoveringMap.existsUnique_continuousMap_liftsstatement and proof · cited by 1
- ContinuousMap.HomotopyEquiv.simplyConnectedSpacestatement and proof · cited by 1
- ContinuousMap.HomotopyEquiv.simplyConnectedSpace_iffstatement and proof · cited by 1
- SimplyConnectedSpace.casesOnstatement and proof · cited by 1
- SimplyConnectedSpace.equiv_unitstatement and proof · cited by 1