Theorems · Theorem · functional analysis
WithSeminorms.partial_sups
∀ {𝕜 : Type u_2} {E : Type u_6} {ι : Type u_9} [inst : NormedField 𝕜] [inst_1 : AddCommGroup E] [inst_2 : Module 𝕜 E]
[inst_3 : Preorder ι] [inst_4 : LocallyFiniteOrderBot ι] {p : SeminormFamily 𝕜 E ι} [inst_5 : TopologicalSpace E],
WithSeminorms p → WithSeminorms fun i => (Finset.Iic i).sup p- Cited by
- 1 results in Mathlib
- Foundations
- Depth 167 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites21
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
- Preorderstatement and proof · cited by 7,952
- NNRealproof · cited by 4,310
- le_reflproof · cited by 2,061
- le_rflproof · cited by 1,558
- one_smulproof · cited by 1,374
- NormedFieldstatement and proof · cited by 1,084
- LinearMap.idproof · cited by 625
- Finset.supstatement and proof · cited by 530
- LocallyFiniteOrderBotstatement and proof · cited by 286
Cited by1
Results whose statement or proof uses this declaration.
- ContDiffMapSupportedIn.withSeminorms'proof · cited by 0