Theorems · Theorem · functional analysis

Submodule.projectionOntoL_apply_eq_zero_iff

∀ {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} (h : Submodule.IsTopCompl p q) {x : M},
  (p.projectionOntoL q h) x = 0 ↔ x ∈ q

Defined in

Mathlib.Topology.Algebra.Module.Complement

Cited by

1 results in Mathlib

Foundations

Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingTopologicalSpaceAddCommGroupModule