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Theorems · Definition · functional analysis

GroupSeminorm.toSeminormedGroup

{E : Type u_5} → [inst : Group E] → GroupSeminorm E → SeminormedGroup E

Construct a seminormed group from a seminorm, i.e., registering the pseudodistance and the pseudometric space structure from the seminorm properties. Note that in most cases this instance creates bad definitional equalities (e.g., it does not take into account a possibly existing UniformSpace instance on E).

Defined in
Mathlib.Analysis.Normed.Group.Defs
Cited by
0 results in Mathlib
Foundations
Depth 113 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
Group
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GroupNorm.toNormedGroup · cited by 0GroupNorm.toNormedGroupGroupSeminorm.toSeminormedCommGroup · cited by 0GroupSeminorm.toSeminorme…Group · cited by 6238GroupSeminormedGroup · cited by 250SeminormedGroupGroupSeminorm · cited by 39GroupSeminormGroupSeminorm.toSeminormedGro…CITED BYCITES

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