Theorems · Theorem · Lie groups
map_mul_left_nhds_one
∀ {G : Type w} [inst : TopologicalSpace G] [inst_1 : Group G] [IsTopologicalGroup G] (x : G),
Filter.map (fun x_1 => x * x_1) (nhds 1) = nhds x- Defined in
- Mathlib.Topology.Algebra.Group.Basic
- Cited by
- 4 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
- Filterstatement · cited by 8,121
- Groupstatement and proof · cited by 6,238
- nhdsstatement and proof · cited by 5,554
- mul_oneproof · cited by 3,885
- Filter.mapstatement · cited by 819
- IsTopologicalGroupstatement and proof · cited by 469
- map_mul_left_nhdsproof · cited by 2
Cited by4
Results whose statement or proof uses this declaration.
- continuous_of_tendsto_nhds_oneproof · cited by 1
- IsTopologicalGroup.isOpenMap_iff_nhds_oneproof · cited by 1
- continuous_of_continuousAt_one₂proof · cited by 0
- nhds_mulproof · cited by 0