Theorems · Definition · functional analysis
GroupNorm.toNormedGroup
{E : Type u_5} → [inst : Group E] → GroupNorm E → NormedGroup EConstruct a normed group from a norm, i.e., registering the distance and the metric space
structure from the norm 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 115 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Group
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Groupstatement and proof · cited by 6,238
- SeminormedGroupproof · cited by 250
- NormedGroupstatement · cited by 18
- GroupNormstatement and proof · cited by 15
- SeminormedGroup.dist_eqproof · cited by 2
- GroupNorm.toGroupSeminormproof · cited by 2
- GroupSeminorm.toSeminormedGroupproof · cited by 0
Cited by1
Results whose statement or proof uses this declaration.
- GroupNorm.toNormedCommGroupproof · cited by 0