Prove2Me

`BookProof.ChapterSeparableSpectrum.metrizableSpace_characterSpace` [SeparableSpace A] : MetrizableSpace (characterSpace ℂ A)

Proved
BookProof.ChapterSeparableSpectrum.metrizableSpace_characterSpace

by leonardopedro · Oct 17, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterSeparableSpectrum.

BookProof.ChapterSeparableSpectrum.metrizableSpace_characterSpace [SeparableSpace A] : MetrizableSpace (characterSpace ℂ A)

Formalization note: Lean 4 identifier BookProof.ChapterSeparableSpectrum.metrizableSpace_characterSpace.

Preamble
-- Generated from ChapterSeparableSpectrum.lean — theorem BookProof.ChapterSeparableSpectrum.metrizableSpace_characterSpace
import Definitions.Def_ChapterAbelianGelfandModel
import Definitions.Def_ChapterAbelianDirectSum
import Definitions.Def_ChapterStandardBorelClassification
import Mathlib
import Definitions.Def_ChapterSeparableSpectrum
open BookProof.ChapterSeparableSpectrum


noncomputable section

open MeasureTheory TopologicalSpace WeakDual


open BookProof.ChapterAbelianGelfandModel BookProof.ChapterAbelianDirectSum
open BookProof.ChapterStandardBorelClassification

variable (Y : Type*) [TopologicalSpace Y] [CompactSpace Y] [T2Space Y]
variable {Y : Type*} [TopologicalSpace Y] [CompactSpace Y] [T2Space Y]
  [SeparableSpace C(Y, ℂ)] [MeasurableSpace Y] [BorelSpace Y]
variable {H : Type*} [NormedAddCommGroup H] [InnerProductSpace ℂ H] [CompleteSpace H]
variable (A : Type*) [CommCStarAlgebra A]
Formal statement
theorem BookProof.ChapterSeparableSpectrum.metrizableSpace_characterSpace [SeparableSpace A] :
    MetrizableSpace (characterSpace ℂ A) := by sorry

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