Theorems · Definition · general topology

Filter.zeroAtFilterSubmodule

(𝕜 : Type u_1) →
  {α : Type u_2} →
    {β : Type u_3} →
      [inst : TopologicalSpace β] →
        [inst_1 : Semiring 𝕜] →
          [inst_2 : AddCommMonoid β] →
            [inst_3 : Module 𝕜 β] → [ContinuousAdd β] → [ContinuousConstSMul 𝕜 β] → Filter α → Submodule 𝕜 (α → β)

zeroAtFilterSubmodule l is the submodule of f : α → β which tend to zero along l.

Defined in

Mathlib.Order.Filter.ZeroAndBoundedAtFilter

Cited by

0 results in Mathlib

Foundations

Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceSemiringAddCommMonoidModuleContinuousAddContinuousConstSMul