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Theorems · Definition · functional analysis

NormedGroup.ofSeparation

{E : Type u_5} → [inst : SeminormedGroup E] → (∀ (x : E), ‖x‖ = 0 → x = 1) → NormedGroup E

Construct a NormedGroup from a SeminormedGroup satisfying ∀ x, ‖x‖ = 0 → x = 1. This avoids having to go back to the (Pseudo)MetricSpace level when declaring a NormedGroup instance as a special case of a more general SeminormedGroup instance.

Defined in
Mathlib.Analysis.Normed.Group.Defs
Cited by
0 results in Mathlib
Foundations
Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
SeminormedGroup
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Around this declaration

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NormedCommGroup.ofSeparation · cited by 0NormedCommGroup.ofSeparat…Real · cited by 25697RealNorm.norm · cited by 5413Norm.normMetricSpace · cited by 1684MetricSpaceSeminormedGroup · cited by 250SeminormedGroupNormedGroup · cited by 18NormedGroupSeminormedGroup.dist_eq · cited by 2SeminormedGroup.dist_eqNormedGroup.ofSeparationCITED BYCITES

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