Theorems · Theorem · functional analysis

Seminorm.ball_subset_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 : E) (r : ℝ), p.ball x r ⊆ p.closedBall x r

Defined in

Mathlib.Analysis.Seminorm

Cited by

5 results in Mathlib

Foundations

Depth 102 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SeminormedRingAddCommGroupSMul