Theorems · Definition · functional analysis
GroupSeminorm.toSeminormedCommGroup
{E : Type u_5} → [inst : CommGroup E] → GroupSeminorm E → SeminormedCommGroup EConstruct 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 114 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommGroup
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.
- CommGroupstatement and proof · cited by 990
- SeminormedGroupproof · cited by 250
- SeminormedCommGroupstatement · cited by 191
- GroupSeminormstatement and proof · cited by 39
- SeminormedGroup.dist_eqproof · cited by 2
- GroupSeminorm.toSeminormedGroupproof · cited by 0
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