Theorems · Definition · functional analysis
SeminormedCommGroup.ofMulDist
{E : Type u_5} →
[inst : Norm E] →
[inst_1 : CommGroup E] →
[inst_2 : PseudoMetricSpace E] →
(∀ (x : E), ‖x‖ = dist 1 x) → (∀ (x y z : E), dist x y ≤ dist (z * x) (z * y)) → SeminormedCommGroup EConstruct a seminormed group from a multiplication-invariant pseudodistance.
- Defined in
- Mathlib.Analysis.Normed.Group.Defs
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 103 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites10
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
- PseudoMetricSpacestatement and proof · cited by 1,550
- Dist.diststatement and proof · cited by 1,539
- CommGroupstatement and proof · cited by 990
- Normstatement and proof · cited by 512
- SeminormedGroupproof · cited by 250
- SeminormedCommGroupstatement · cited by 191
- SeminormedGroup.dist_eqproof · cited by 2
- SeminormedGroup.ofMulDistproof · cited by 0
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