Theorems · Definition · functional analysis

WeakDual

(𝕜 : Type u_6) →
  (E : Type u_7) →
    [inst : CommSemiring 𝕜] →
      [inst_1 : TopologicalSpace 𝕜] →
        [ContinuousAdd 𝕜] →
          [ContinuousConstSMul 𝕜 𝕜] →
            [inst_4 : AddCommMonoid E] → [Module 𝕜 E] → [TopologicalSpace E] → Type (max u_6 u_7)

The weak star topology is the topology coarsest topology on E →L[𝕜] 𝕜 such that all functionals fun v => v x are continuous.

Defined in

Mathlib.Topology.Algebra.Module.Spaces.WeakDual

Cited by

103 results in Mathlib

Foundations

Depth 87 from the axioms, rests on 1,124 definitions · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringTopologicalSpaceContinuousAddContinuousConstSMulAddCommMonoidModuleTopologicalSpace