isCompact_nnreal — Mathlib

English

There is a spectrum for NNReal that is compact when the Real-spectrum is compact.

Русский

Существует спектр для NNReal, который компактен при компактости Real-спектра.

LaTeX

$$IsCompact(\\sigma_{\\mathbb{R}_{≥0}}(a))$$

Lean4

@[simp]
theorem isCompact_nnreal {A : Type*} [NormedRing A] [NormedAlgebra ℝ A] (a : A) [CompactSpace (spectrum ℝ a)] :
    IsCompact (spectrum ℝ≥0 a) := by
  rw [isCompact_iff_compactSpace]
  infer_instance

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