Theorems · Theorem · functional analysis

SeminormFamily.basisSets_iff

∀ {R : Type u_1} {E : Type u_6} {ι : Type u_9} [inst : SeminormedRing R] [inst_1 : AddCommGroup E] [inst_2 : Module R E]
  (p : SeminormFamily R E ι) {U : Set E}, U ∈ p.basisSets ↔ ∃ i r, 0 < r ∧ U = (i.sup p).ball 0 r

Defined in

Mathlib.Analysis.LocallyConvex.WithSeminorms

Cited by

16 results in Mathlib

Foundations

Depth 118 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SeminormedRingAddCommGroupModule