Theorems · Theorem · functional analysis
PolynormableSpace.withSeminorms
∀ (𝕜 : Type u_2) (E : Type u_6) [inst : NormedField 𝕜] [inst_1 : AddCommGroup E] [inst_2 : Module 𝕜 E] [inst_3 : TopologicalSpace E] [PolynormableSpace 𝕜 E], WithSeminorms fun p => ↑p
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 115 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- Continuousstatement · cited by 2,592
- NormedFieldstatement and proof · cited by 1,084
- Seminormstatement · cited by 272
- WithSeminormsstatement · cited by 69
- PolynormableSpacestatement and proof · cited by 15
- PolynormableSpace.withSeminorms'proof · cited by 2
Cited by6
Results whose statement or proof uses this declaration.
- Module.Dual.exists_continuous_extension_of_le_seminormproof · cited by 2
- Seminorm.exists_le_comp_of_isInducingproof · cited by 1
- Module.Dual.exists_continuous_extension_of_le_seminorm_realproof · cited by 0
- Topology.IsInducing.polynormableSpaceproof · cited by 0
- PolynormableSpace.banach_steinhausproof · cited by 0
- PolynormableSpace.inducedproof · cited by 0