Theorems · Definition · algebraic topology
HomotopyGroup.pi1EquivFundamentalGroup
{X : Type u_2} → [inst : TopologicalSpace X] → {x : X} → HomotopyGroup.Pi 1 X x ≃ FundamentalGroup X xThe first homotopy group at x is in bijection with the fundamental group.
- Defined in
- Mathlib.Topology.Homotopy.HomotopyGroup
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 163 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.
Cites5
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
- Equivstatement · cited by 8,337
- FundamentalGroupstatement · cited by 30
- HomotopyGroup.Pistatement · cited by 0
- homotopyGroupEquivFundamentalGroupOfUniqueproof · cited by 0
Cited by1
Results whose statement or proof uses this declaration.
- HomotopyGroup.pi1MulEquivFundamentalGroupproof · cited by 0