Theorems · Theorem · functional analysis
gaugeSeminormFamily_ball
∀ {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] [inst_5 : IsScalarTower ℝ 𝕜 E] [inst_6 : ContinuousSMul ℝ E]
(s : AbsConvexOpenSets 𝕜 E), (gaugeSeminormFamily 𝕜 E s).ball 0 1 = ↑s- Cited by
- 1 results in Mathlib
- Foundations
- Depth 166 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites23
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- 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
- Set.ofPredproof · cited by 6,101
- IsScalarTowerstatement and proof · cited by 3,896
- RCLikestatement and proof · cited by 2,829
- IsOpenstatement · cited by 2,400
- ContinuousSMulstatement and proof · cited by 1,016
- RCLike.toPartialOrderstatement · cited by 106
- Seminorm.ballstatement · cited by 78
Cited by1
Results whose statement or proof uses this declaration.
- with_gaugeSeminormFamilyproof · cited by 0