Theorems · Definition · functional analysis
normSeminorm
(𝕜 : Type u_3) →
(E : Type u_7) →
[inst : NormedField 𝕜] → [inst_1 : SeminormedAddCommGroup E] → [inst_2 : NormedSpace 𝕜 E] → Seminorm 𝕜 EThe norm of a seminormed group as a seminorm.
- Defined in
- Mathlib.Analysis.Seminorm
- Cited by
- 32 results in Mathlib
- Foundations
- Depth 121 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- NormedSpacestatement and proof · cited by 12,499
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- NormedFieldstatement and proof · cited by 1,084
- Seminormstatement · cited by 272
- AddGroupSeminormproof · cited by 50
- normAddGroupSeminormproof · cited by 1
Cited by34
Results whose statement or proof uses this declaration.
- ContDiffMapSupportedIn.seminormproof · cited by 15
- norm_withSeminormsstatement and proof · cited by 12
- ball_normSeminormstatement and proof · cited by 7
- LinearMap.toSeminormproof · cited by 6
- NormedSpace.isVonNBounded_of_isBoundedproof · cited by 4
- WithSeminorms.continuous_normedSpace_rngstatement and proof · cited by 4
- Seminorm.bound_of_continuous_normedSpaceproof · cited by 3
- absorbent_ball_zeroproof · cited by 3
- rescale_to_shell_semi_normedproof · cited by 3
- PiTensorProduct.injectiveSeminorm_defstatement and proof · cited by 3
- Module.Dual.exists_continuous_extension_of_le_seminormproof · cited by 2
- NormedSpace.equicontinuous_TFAEproof · cited by 2