English
The homeomorphism QuasispectrumRestricts.homeomorph realizes a topological equivalence between the S- and R-quasispectra via restriction along f.
Русский
Гомеоморфизм QuasispectrumRestricts.homeomorph реализует топологическое эквивалентное отображение между S- и R-кувази-спектрами через ограничение по f.
LaTeX
$$$\\text{QuasispectrumRestricts.homeomorph}$ is a homeomorphism $\\sigma_n(S,a) \\cong_t \\sigma_n(R,a)$.$$
Lean4
/-- This map sends `f : C(X, ℝ)` to `Real.toNNReal ∘ f`, bundled as a continuous map `C(X, ℝ≥0)`. -/
noncomputable def toNNReal (f : C(X, ℝ)) : C(X, ℝ≥0) :=
.realToNNReal |>.comp f