Theorems · Definition · functional analysis

LinearPMap.IsClosed

{R : Type u_1} →
  {E : Type u_2} →
    {F : Type u_3} →
      [inst : CommRing R] →
        [inst_1 : AddCommGroup E] →
          [inst_2 : AddCommGroup F] →
            [inst_3 : Module R E] →
              [inst_4 : Module R F] → [TopologicalSpace E] → [TopologicalSpace F] → (E →ₗ.[R] F) → Prop

An unbounded operator is closed iff its graph is closed.

Defined in

Mathlib.Topology.Algebra.Module.LinearPMap

Cited by

6 results in Mathlib

Foundations

Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupAddCommGroupModuleModuleTopologicalSpaceTopologicalSpace