Theorems · Theorem · functional analysis
SeminormFamily.filter_eq_iInf
∀ {𝕜 : Type u_2} {F : Type u_7} {ι : Type u_9} [inst : NormedDivisionRing 𝕜] [inst_1 : AddCommGroup F]
[inst_2 : Module 𝕜 F] (p : SeminormFamily 𝕜 F ι), p.moduleFilterBasis.filter = ⨅ i, Filter.comap (⇑(p i)) (nhds 0)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 159 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites39
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setproof · cited by 53,352
- Realstatement and proof · cited by 25,697
- Modulestatement and proof · cited by 20,661
- Finsetproof · cited by 13,712
- AddCommGroupstatement and proof · cited by 12,871
- Filterstatement · cited by 8,121
- nhdsstatement and proof · cited by 5,554
- Set.preimageproof · cited by 4,946
- le_antisymmproof · cited by 2,068
- le_reflproof · cited by 2,061
- iInfstatement and proof · cited by 1,690
Cited by1
Results whose statement or proof uses this declaration.
- SeminormFamily.withSeminorms_iff_nhds_eq_iInfproof · cited by 8