Theorems · Theorem · functional analysis
withSeminorms_iInf
∀ {𝕜 : Type u_2} {E : Type u_6} {ι : Type u_9} [inst : NormedField 𝕜] [inst_1 : AddCommGroup E] [inst_2 : Module 𝕜 E]
{κ : ι → Type u_11} {p : (i : ι) → SeminormFamily 𝕜 E (κ i)} {t : ι → TopologicalSpace E},
(∀ (i : ι), WithSeminorms (p i)) → WithSeminorms (SeminormFamily.sigma p)- Cited by
- 3 results in Mathlib
- Foundations
- Depth 164 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement and proof · cited by 24,529
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- iInfstatement and proof · cited by 1,690
- IsTopologicalAddGroupproof · cited by 1,394
- NormedFieldstatement and proof · cited by 1,084
- WithSeminormsstatement and proof · cited by 69
- SeminormFamilystatement and proof · cited by 68
- iInf_congrproof · cited by 15
- WithSeminorms.topologicalAddGroupproof · cited by 11
- topologicalAddGroup_iInfproof · cited by 5
- SeminormFamily.sigmastatement and proof · cited by 3
Cited by3
Results whose statement or proof uses this declaration.
- withSeminorms_piproof · cited by 3
- PolynormableSpace.iInfproof · cited by 1
- ContDiffMapSupportedIn.withSeminormsproof · cited by 1