Theorems · Theorem · functional analysis

Seminorm.mem_closedBall

∀ {𝕜 : Type u_3} {E : Type u_7} [inst : SeminormedRing 𝕜] [inst_1 : AddCommGroup E] [inst_2 : SMul 𝕜 E]
  (p : Seminorm 𝕜 E) {x y : E} {r : ℝ}, y ∈ p.closedBall x r ↔ p (y - x) ≤ r

Defined in

Mathlib.Analysis.Seminorm

Cited by

8 results in Mathlib

Foundations

Depth 101 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SeminormedRingAddCommGroupSMul