range — Mathlib

English

If f is a homeomorphism, NoetherianSpace is preserved in both directions.

Русский

Гомеоморфизм сохраняет свойство Ноetherian как в обе стороны.

LaTeX

$$$\\text{noetherianSpace_iff_of_homeomorph}(f) : NoetherianSpace α \\iff NoetherianSpace β$$$

Lean4

theorem range [NoetherianSpace α] (f : α → β) (hf : Continuous f) : NoetherianSpace (Set.range f) :=
  noetherianSpace_of_surjective (Set.rangeFactorization f) (hf.subtype_mk _) Set.rangeFactorization_surjective

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