Theorems · Theorem · functional analysis

LinearPMap.closureHasCore

∀ {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]
  [inst_7 : ContinuousAdd E] [inst_8 : ContinuousAdd F] [inst_9 : TopologicalSpace R] [inst_10 : ContinuousSMul R E]
  [inst_11 : ContinuousSMul R F] (f : E →ₗ.[R] F), f.closure.HasCore f.domain

For every unbounded operator f the submodule f.domain is a core of its closure. Note that we don't require that f is closable, due to the definition of the closure.

Defined in

Mathlib.Topology.Algebra.Module.LinearPMap

Cited by

0 results in Mathlib

Foundations

Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupAddCommGroupModuleModuleTopologicalSpaceTopologicalSpaceContinuousAddContinuousAddTopologicalSpaceContinuousSMulContinuousSMul