Theorems · Definition · Lie groups
Homeomorph.shearAddRight
(G : Type w) → [inst : TopologicalSpace G] → [inst_1 : AddGroup G] → [IsTopologicalAddGroup G] → G × G ≃ₜ G × G
The map (x, y) ↦ (x, x + y) as a homeomorphism. This is a shear mapping.
- Defined in
- Mathlib.Topology.Algebra.Group.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 75 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
- AddGroupstatement and proof · cited by 4,410
- IsTopologicalAddGroupstatement and proof · cited by 1,394
- Homeomorphstatement · cited by 725
- Equiv.reflproof · cited by 274
- Equiv.addLeftproof · cited by 19
- Equiv.prodShearproof · cited by 5
Cited by2
Results whose statement or proof uses this declaration.
- Homeomorph.shearAddRight_coestatement · cited by 0
- Homeomorph.shearAddRight_symm_coestatement · cited by 0