Theorems · Theorem · functional analysis
WithSeminorms.toPolynormableSpace
∀ {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] {p : SeminormFamily 𝕜 E ι}, WithSeminorms p → PolynormableSpace 𝕜 E- Cited by
- 3 results in Mathlib
- Foundations
- Depth 165 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.coeproof · cited by 62,936
- TopologicalSpacestatement and proof · cited by 24,529
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- nhdsproof · cited by 5,554
- Filter.Tendstoproof · cited by 3,814
- Continuousproof · cited by 2,592
- le_antisymmproof · cited by 2,068
- iInfproof · cited by 1,690
- map_zeroproof · cited by 1,614
- IsTopologicalAddGroupproof · cited by 1,394
- NormedFieldstatement and proof · cited by 1,084
Cited by3
Results whose statement or proof uses this declaration.
- PolynormableSpace.iInfproof · cited by 1
- Topology.IsInducing.polynormableSpaceproof · cited by 0
- PolynormableSpace.inducedproof · cited by 0