characterSpace — Mathlib

English

As above, a nontrivially normed field 𝕜 yields 𝔠 ≤ #E for nontrivial E with topology and module structure.

Русский

Как выше, для ненулевого нормированного поля 𝕜 выполняется 𝔠 ≤ |E| для любой нетривиальной модульной структуры E.

LaTeX

$$$\\mathfrak{c} \\le |E|$ under the given hypotheses.$$

Lean4

/-- The character space of a topological algebra is the subset of elements of the weak dual that
are also algebra homomorphisms. -/
def characterSpace (𝕜 : Type*) (A : Type*) [CommSemiring 𝕜] [TopologicalSpace 𝕜] [ContinuousAdd 𝕜]
    [ContinuousConstSMul 𝕜 𝕜] [NonUnitalNonAssocSemiring A] [TopologicalSpace A] [Module 𝕜 A] :=
  {φ : WeakDual 𝕜 A | φ ≠ 0 ∧ ∀ x y : A, φ (x * y) = φ x * φ y}

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