Theorems · Theorem · functional analysis

LinearPMap.inverse_closure

∀ {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]
  {f : E →ₗ.[R] F} [inst_7 : ContinuousAdd E] [inst_8 : ContinuousAdd F] [inst_9 : TopologicalSpace R]
  [inst_10 : ContinuousSMul R E] [inst_11 : ContinuousSMul R F],
  f.toFun.ker = ⊥ → f.IsClosable → f.closure.toFun.ker = ⊥ → f.inverse.closure = f.closure.inverse

If f is invertible and closable, then taking the closure and the inverse commute.

Defined in

Mathlib.Topology.Algebra.Module.LinearPMap

Cited by

0 results in Mathlib

Foundations

Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupAddCommGroupModuleModuleTopologicalSpaceTopologicalSpaceContinuousAddContinuousAddTopologicalSpaceContinuousSMulContinuousSMul