gaugeSeminormFamily — Mathlib

English

The ball of the gauge seminorm at radius 1 coincides with the underlying set.

Русский

Шар шкалы-гейнджа семинормы радиуса 1 совпадает с базовым множеством.

LaTeX

$$$(gaugeSeminormFamily 𝕜 E s).ball 0 1 = (s : Set E)$$$

Lean4

/-- The family of seminorms defined by the gauges of absolute convex open sets. -/
noncomputable def gaugeSeminormFamily : SeminormFamily 𝕜 E (AbsConvexOpenSets 𝕜 E) := fun s =>
  gaugeSeminorm s.coe_balanced s.coe_convex (absorbent_nhds_zero s.coe_nhds)

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