isEmbedding_iff_isInducing — Mathlib

English

For maps into a T0 space, being a topological embedding is equivalent to being inducing.

Русский

Для отображений в T0-пространство быть топологическим вложением эквивалентно being inducing.

LaTeX

$$$IsEmbedding(f) \iff IsInducing(f)\,$ (under [TopologicalSpace Y] [T0Space X]).$$

Lean4

theorem isEmbedding_iff_isInducing [TopologicalSpace Y] [T0Space X] {f : X → Y} : IsEmbedding f ↔ IsInducing f :=
  ⟨IsEmbedding.isInducing, IsInducing.isEmbedding⟩

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