Theorems · Definition · group theory
AddUnits.embedProduct
(α : Type u_6) → [inst : AddMonoid α] → AddUnits α →+ α × αᵃᵒᵖ
Canonical homomorphism of additive monoids from AddUnits α into α × αᵃᵒᵖ.
Used mainly to define the natural topology of AddUnits α.
- Defined in
- Mathlib.Algebra.Group.Prod
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 23 from the axioms · uses propext, Quot.sound
- Assumes
- AddMonoid
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.
- AddMonoidHomstatement · cited by 3,230
- AddMonoidstatement and proof · cited by 2,864
- AddOppositestatement · cited by 452
- AddUnitsstatement and proof · cited by 325
- AddUnits.valproof · cited by 248
- AddOpposite.opproof · cited by 192
Cited by9
Results whose statement or proof uses this declaration.
- AddUnits.isInducing_embedProductstatement · cited by 4
- AddUnits.continuous_embedProductstatement · cited by 3
- AddUnits.isEmbedding_embedProductstatement · cited by 2
- AddUnits.embedProduct_applystatement and proof · cited by 1
- AddUnits.embedProduct_injectivestatement and proof · cited by 1
- AddUnits.range_embedProductstatement and proof · cited by 1
- AddUnits.topology_eq_infproof · cited by 1
- AddUnits.isClosedEmbedding_embedProductstatement and proof · cited by 0
- AddUnits.isOpenMap_mapproof · cited by 0