Theorems · Definition · functional analysis

LinearPMap.IsClosable

{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] →
                [inst_5 : TopologicalSpace E] →
                  [inst_6 : TopologicalSpace F] →
                    [ContinuousAdd E] →
                      [ContinuousAdd F] →
                        [inst_9 : TopologicalSpace R] →
                          [ContinuousSMul R E] → [ContinuousSMul R F] → (E →ₗ.[R] F) → Prop

An unbounded operator is closable iff the closure of its graph is a graph.

Defined in

Mathlib.Topology.Algebra.Module.LinearPMap

Cited by

15 results in Mathlib

Foundations

Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupAddCommGroupModuleModuleTopologicalSpaceTopologicalSpaceContinuousAddContinuousAddTopologicalSpaceContinuousSMulContinuousSMul