cobounded_eq_aux — Mathlib

English

The uniformity on Unitization is the pullback of the product uniformity via addEquiv; i.e., coboundedness agrees under this map.

Русский

Униформность на Unitization совпадает с обратной кривой по произведению через addEquiv; то есть согласуется cobounded.

LaTeX

$$$$\\mathcal{U}_{\\text{Unitization}} = \\mathrm{comap}\\big(\\mathrm{addEquiv}\\ 𝕜 A\\big)(\\mathcal{U}_{𝕜\\times A}).$$$$

Lean4

theorem cobounded_eq_aux : @cobounded _ (Bornology.induced <| addEquiv 𝕜 A) = cobounded (Unitization 𝕜 A) :=
  le_antisymm lipschitzWith_addEquiv.comap_cobounded_le antilipschitzWith_addEquiv.tendsto_cobounded.le_comap

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