comap_norm_nhds_one — Mathlib

English

The preimage under the norm map of the neighborhood of 0 in the reals is the neighborhood of 1 in E: comap norm (nhds 0) = nhds (1).

Русский

Образ предобразной карты нормы: предобразNeighborhood(0) по норме совпадает с окрестностью единицы в E.

LaTeX

$$$\mathrm{comap}_{\|\cdot\|}(\mathcal{N}_0) = \mathcal{N}_1$$$

Lean4

@[to_additive (attr := simp 1100)]
theorem comap_norm_nhds_one : comap norm (𝓝 0) = 𝓝 (1 : E) := by
  simpa only [dist_one_right] using nhds_comap_dist (1 : E)

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