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Theorems · Definition · functional analysis

SeminormedAddGroup.ofAddDist

{E : Type u_5} →
  [inst : Norm E] →
    [inst_1 : AddGroup E] →
      [inst_2 : PseudoMetricSpace E] →
        (∀ (x : E), ‖x‖ = dist 0 x) → (∀ (x y z : E), dist x y ≤ dist (z + x) (z + y)) → SeminormedAddGroup E

Construct a seminormed group from a translation-invariant distance.

Defined in
Mathlib.Analysis.Normed.Group.Defs
Cited by
0 results in Mathlib
Foundations
Depth 102 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
NormAddGroupPseudoMetricSpace
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SeminormedAddCommGroup.ofAddDist · cited by 0SeminormedAddCommGroup.of…NormedAddGroup.ofAddDist · cited by 0NormedAddGroup.ofAddDistReal · cited by 25697RealNorm.norm · cited by 5413Norm.normAddGroup · cited by 4410AddGroupPseudoMetricSpace · cited by 1550PseudoMetricSpaceDist.dist · cited by 1539Dist.distNorm · cited by 512NormSeminormedAddGroup · cited by 331SeminormedAddGroupSeminormedAddGroup.ofAddDistCITED BYCITES

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Cited by2

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