Theorems · Theorem · functional analysis

locallyConvexSpace_iff_exists_convex_subset_zero

∀ (𝕜 : Type u_1) (E : Type u_2) [inst : Semiring 𝕜] [inst_1 : PartialOrder 𝕜] [inst_2 : AddCommGroup E]
  [inst_3 : Module 𝕜 E] [inst_4 : TopologicalSpace E] [IsTopologicalAddGroup E],
  LocallyConvexSpace 𝕜 E ↔ ∀ U ∈ nhds 0, ∃ S ∈ nhds 0, Convex 𝕜 S ∧ S ⊆ U

Defined in

Mathlib.Topology.Algebra.Module.LocallyConvex

Cited by

1 results in Mathlib

Foundations

Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringPartialOrderAddCommGroupModuleTopologicalSpaceIsTopologicalAddGroup