isUniformEmbedding_iff' — Mathlib

English

UniformEmbedding f iff Injective f, UniformContinuous f, and comap condition.

Русский

UniformEmbedding f тогда равносильно инъективности, равномерной непрерывности и условия комапы.

LaTeX

$$$IsUniformEmbedding f \\iff Injective f \\land UniformContinuous f \\land comap (Prod.map f f) (\\mathcal{U} β) \\le \\mathcal{U} α$$$

Lean4

theorem isUniformEmbedding_iff' {f : α → β} :
    IsUniformEmbedding f ↔ Injective f ∧ UniformContinuous f ∧ comap (Prod.map f f) (𝓤 β) ≤ 𝓤 α := by
  rw [isUniformEmbedding_iff, and_comm, isUniformInducing_iff']

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