Theorems · Definition · functional analysis
gaugeSeminormFamily
(𝕜 : Type u_1) →
(E : Type u_2) →
[inst : RCLike 𝕜] →
[inst_1 : AddCommGroup E] →
[inst_2 : TopologicalSpace E] →
[inst_3 : Module 𝕜 E] →
[inst_4 : Module ℝ E] →
[IsScalarTower ℝ 𝕜 E] → [ContinuousSMul ℝ E] → SeminormFamily 𝕜 E (AbsConvexOpenSets 𝕜 E)The family of seminorms defined by the gauges of absolute convex open sets.
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 165 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- TopologicalSpacestatement and proof · cited by 24,529
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- IsScalarTowerstatement and proof · cited by 3,896
- RCLikestatement and proof · cited by 2,829
- ContinuousSMulstatement and proof · cited by 1,016
- RCLike.toPartialOrderstatement · cited by 106
- SeminormFamilystatement · cited by 68
- AbsConvexOpenSetsstatement and proof · cited by 8
- gaugeSeminormproof · cited by 6
Cited by3
Results whose statement or proof uses this declaration.
- gaugeSeminormFamily_ballstatement · cited by 1
- gaugeSeminormFamily.congr_simpstatement and proof · cited by 0
- with_gaugeSeminormFamilystatement and proof · cited by 0