Theorems · Definition · functional analysis
NormedAddGroup.ofSeparation
{E : Type u_5} → [inst : SeminormedAddGroup E] → (∀ (x : E), ‖x‖ = 0 → x = 0) → NormedAddGroup EConstruct a NormedAddGroup from a SeminormedAddGroup
satisfying ∀ x, ‖x‖ = 0 → x = 0. This avoids having to go back to the (Pseudo)MetricSpace
level when declaring a NormedAddGroup instance as a special case of a more general
SeminormedAddGroup 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
- SeminormedAddGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- Norm.normstatement and proof · cited by 5,413
- MetricSpaceproof · cited by 1,684
- SeminormedAddGroupstatement and proof · cited by 331
- NormedAddGroupstatement · cited by 32
- SeminormedAddGroup.dist_eqproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- NormedAddCommGroup.ofSeparationproof · cited by 0