Theorems · Theorem · functional analysis
SeminormFamily.withSeminorms_iff_nhds_eq_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]
[t : TopologicalSpace E] [IsTopologicalAddGroup E] (p : SeminormFamily 𝕜 E ι),
WithSeminorms p ↔ nhds 0 = ⨅ i, Filter.comap (⇑(p i)) (nhds 0)- Cited by
- 8 results in Mathlib
- Foundations
- Depth 160 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites22
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Realstatement · 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
- Filterstatement and proof · cited by 8,121
- nhdsstatement and proof · cited by 5,554
- iInfstatement · cited by 1,690
- IsTopologicalAddGroupstatement and proof · cited by 1,394
- NormedFieldstatement and proof · cited by 1,084
- Filter.comapstatement · cited by 546
- Seminormstatement · cited by 272
Cited by8
Results whose statement or proof uses this declaration.
- norm_withSeminormsproof · cited by 12
- LinearMap.withSeminorms_inducedproof · cited by 5
- WithSeminorms.continuous_of_continuous_compproof · cited by 3
- SeminormFamily.withSeminorms_iff_topologicalSpace_eq_iInfproof · cited by 3
- WithSeminorms.toPolynormableSpaceproof · cited by 3
- SeminormFamily.withSeminorms_iff_uniformSpace_eq_iInfproof · cited by 1
- WithSeminorms.firstCountableTopologyproof · cited by 0
- schwartz_withSeminormsproof · cited by 0