Theorems · Theorem · Lie groups
AddMonoidHom.isStrictMap_iff_isEmbedding_kerLift
∀ {G : Type u_1} {H : Type u_2} [inst : AddGroup G] [inst_1 : AddGroup H] {f : G →+ H} [inst_2 : TopologicalSpace G]
[inst_3 : TopologicalSpace H], Topology.IsStrictMap ⇑f ↔ Topology.IsEmbedding ⇑(QuotientAddGroup.kerLift f)An additive group homomorphism is strict if and only if its
QuotientAddGroup.kerLift is an embedding.
- Defined in
- Mathlib.Topology.Maps.Strict.Group
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- TopologicalSpacestatement and proof · cited by 24,529
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement and proof · cited by 3,232
- AddMonoidHomstatement and proof · cited by 3,230
- HasQuotient.Quotientstatement and proof · cited by 2,301
- Topology.IsEmbeddingstatement · cited by 294
- AddMonoidHom.kerstatement and proof · cited by 158
- Topology.IsStrictMapstatement and proof · cited by 45
- Topology.IsQuotientMap.isStrictMap_iffproof · cited by 8
- QuotientAddGroup.kerLiftstatement and proof · cited by 5
- QuotientAddGroup.isQuotientMap_mkproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- LinearMap.isStrictMap_iff_isEmbedding_liftQ_kerproof · cited by 0