Theorems · Theorem · functional analysis

Seminorm.preimage_metric_ball

∀ {𝕜 : Type u_3} {E : Type u_7} [inst : SeminormedRing 𝕜] [inst_1 : AddCommGroup E] [inst_2 : Module 𝕜 E]
  (p : Seminorm 𝕜 E) {r : ℝ}, ⇑p ⁻¹' Metric.ball 0 r = {x | p x < r}

Defined in

Mathlib.Analysis.Seminorm

Cited by

1 results in Mathlib

Foundations

Depth 157 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SeminormedRingAddCommGroupModule