Theorems · Theorem · Lie groups

AddMonoidHom.isStrictMap_iff_isHomeomorph_quotientKerEquivRange

∀ {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 ↔ IsHomeomorph ⇑(QuotientAddGroup.quotientKerEquivRange f)

An additive group homomorphism is strict if and only if the canonical isomorphism G ⧸ f.ker ≃ f.range is a homeomorphism.

Defined in

Mathlib.Topology.Maps.Strict.Group

Cited by

0 results in Mathlib

Foundations

Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddGroupAddGroupTopologicalSpaceTopologicalSpace