Theorems · Theorem · functional analysis

WeakSpace.isOpen_of_isOpen

∀ {𝕜 : Type u_2} {E : Type u_4} [inst : CommSemiring 𝕜] [inst_1 : TopologicalSpace 𝕜] [inst_2 : ContinuousAdd 𝕜]
  [inst_3 : ContinuousConstSMul 𝕜 𝕜] [inst_4 : AddCommMonoid E] [inst_5 : Module 𝕜 E] [inst_6 : TopologicalSpace E]
  (V : Set E), IsOpen (⇑(toWeakSpaceCLM 𝕜 E) '' V) → IsOpen V

A set in E which is open in the weak topology is open.

Defined in

Mathlib.Topology.Algebra.Module.Spaces.WeakDual

Cited by

0 results in Mathlib

Foundations

Depth 101 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringTopologicalSpaceContinuousAddContinuousConstSMulAddCommMonoidModuleTopologicalSpace