Theorems · Definition · Lie groups
Homeomorph.mulLeft
{G : Type w} → [inst : TopologicalSpace G] → [inst_1 : Group G] → [SeparatelyContinuousMul G] → G → G ≃ₜ GMultiplication from the left in a topological group as a homeomorphism.
- Defined in
- Mathlib.Topology.Algebra.Group.Basic
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- Groupstatement and proof · cited by 6,238
- Equiv.Permproof · cited by 1,375
- Homeomorphstatement · cited by 725
- SeparatelyContinuousMulstatement and proof · cited by 133
- Equiv.mulLeftproof · cited by 19
Cited by14
Results whose statement or proof uses this declaration.
- isOpenMap_mul_leftproof · cited by 2
- map_mul_left_nhdsproof · cited by 2
- MeasureTheory.Content.innerContent_pos_of_is_mul_left_invariantproof · cited by 1
- isClosedMap_mul_leftproof · cited by 1
- MeasureTheory.Content.is_mul_left_invariant_innerContentstatement and proof · cited by 1
- smul_connectedComponentproof · cited by 1
- Homeomorph.mulLeft.congr_simpstatement and proof · cited by 0
- Homeomorph.coe_mulLeftstatement · cited by 0
- MeasureTheory.Content.is_mul_left_invariant_outerMeasureproof · cited by 0
- nhds_translation_inv_mulproof · cited by 0
- Filter.map_mul_left_nhdsGTproof · cited by 0
- Filter.map_mul_left_nhdsLTproof · cited by 0