Theorems · Definition · Lie groups
toUnits_homeomorph
{G : Type w} → [inst : Group G] → [inst_1 : TopologicalSpace G] → [ContinuousInv G] → G ≃ₜ GˣIf G is a group with topological ⁻¹, then it is homeomorphic to its units.
- Defined in
- Mathlib.Topology.Algebra.Group.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- Equivproof · cited by 8,337
- Groupstatement and proof · cited by 6,238
- Unitsstatement and proof · cited by 2,804
- Homeomorphstatement · cited by 725
- MulEquiv.toEquivproof · cited by 126
- ContinuousInvstatement and proof · cited by 89
- toUnitsproof · cited by 8
Cited by1
Results whose statement or proof uses this declaration.
- Units.isEmbedding_valproof · cited by 0