isImmersion_eq_inf — Mathlib

English

An immersion f is equivalent to the infimum of two properties: being a preimmersion and having locally closed image of range.

Русский

Вложение f эквивалентно некоему пересечению свойств: being a preimmersion и локально замкнутый образ образа.

LaTeX

$$$\\text{IsImmersion}(f) \\iff \\big(\\text{IsPreimmersion}(f) \\land \\text{IsLocallyClosed}(\\text{range}(f))\\big)$$$

Lean4

theorem isImmersion_eq_inf :
    @IsImmersion =
      (@IsPreimmersion ⊓ topologically fun {_ _} _ _ f ↦ IsLocallyClosed (Set.range f) : MorphismProperty Scheme) :=
  by ext; exact isImmersion_iff _

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