Theorems · Definition · functional analysis

Submodule.projectionOntoL

{R : Type u_1} →
  [inst : Ring R] →
    {M : Type u_2} →
      [inst_1 : TopologicalSpace M] →
        [inst_2 : AddCommGroup M] →
          [inst_3 : Module R M] → (p q : Submodule R M) → Submodule.IsTopCompl p q → M →L[R] ↥p

If h : IsTopCompl p q, h.projectionOnto is the continuous linear projection M →L[R] p along q. This is the continuous version of Submodule.linearProjOfIsCompl. See also Submodule.IsTopCompl.projection for the same projection as an element of M →L[R] M.

Defined in

Mathlib.Topology.Algebra.Module.Complement

Cited by

20 results in Mathlib

Foundations

Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingTopologicalSpaceAddCommGroupModule