Theorems · Definition · functional analysis

Seminorm.ball

{𝕜 : Type u_3} →
  {E : Type u_7} →
    [inst : SeminormedRing 𝕜] → [inst_1 : AddCommGroup E] → [inst_2 : SMul 𝕜 E] → Seminorm 𝕜 E → E → ℝ → Set E

The ball of radius r at x with respect to seminorm p is the set of elements y with p (y - x) < r.

Defined in

Mathlib.Analysis.Seminorm

Cited by

78 results in Mathlib

Foundations

Depth 100 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SeminormedRingAddCommGroupSMul