Theorems · Theorem · functional analysis

Submodule.prodEquivOfIsTopCompl_symm_apply

∀ {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} [inst_4 : IsTopologicalAddGroup M] (h : Submodule.IsTopCompl p q) (x : M),
  (p.prodEquivOfIsTopCompl q h).symm x = ((p.projectionOntoL q h) x, (q.projectionOntoL p ⋯) x)

Defined in

Mathlib.Topology.Algebra.Module.Complement

Cited by

0 results in Mathlib

Foundations

Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingTopologicalSpaceAddCommGroupModuleIsTopologicalAddGroup