Theorems · Definition · functional analysis

ContinuousLinearEquiv.quotKerEquivRange

{R : Type u_1} →
  {M : Type u_3} →
    {Nₗ : Type u_5} →
      [inst : Ring R] →
        [inst_1 : AddCommGroup M] →
          [inst_2 : AddCommGroup Nₗ] →
            [inst_3 : Module R M] →
              [inst_4 : Module R Nₗ] →
                {fₗ : M →ₗ[R] Nₗ} →
                  [inst_5 : TopologicalSpace M] →
                    [inst_6 : TopologicalSpace Nₗ] → Topology.IsStrictMap ⇑fₗ → (M ⧸ fₗ.ker) ≃L[R] ↥fₗ.range

The isomorphism of topological modules M ⧸ f.ker ≃ f.range given by a strict linear map f : M → N. This is an avatar of the first isomorphism theorem.

Defined in

Mathlib.Topology.Maps.Strict.Module

Cited by

1 results in Mathlib

Foundations

Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingAddCommGroupAddCommGroupModuleModuleTopologicalSpaceTopologicalSpace