Theorems · Definition · functional analysis

Submodule.topologicalClosure

{R : Type u} →
  {M : Type v} →
    [inst : Semiring R] →
      [inst_1 : TopologicalSpace M] →
        [inst_2 : AddCommMonoid M] →
          [inst_3 : Module R M] → [ContinuousConstSMul R M] → [ContinuousAdd M] → Submodule R M → Submodule R M

The (topological-space) closure of a submodule of a topological R-module M is itself a submodule.

Defined in

Mathlib.Topology.Algebra.Module.Basic

Cited by

50 results in Mathlib

Foundations

Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringTopologicalSpaceAddCommMonoidModuleContinuousConstSMulContinuousAdd