Theorems · Inductive type · functional analysis
WithSeminorms
{𝕜 : Type u_2} →
{E : Type u_6} →
{ι : Type u_9} →
[inst : NormedField 𝕜] →
[inst_1 : AddCommGroup E] →
[inst_2 : Module 𝕜 E] → SeminormFamily 𝕜 E ι → [topology : TopologicalSpace E] → PropThe proposition that the topology of E is induced by a family of seminorms p.
- Cited by
- 69 results in Mathlib
- Foundations
- Depth 104 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement · cited by 24,529
- Modulestatement · cited by 20,661
- AddCommGroupstatement · cited by 12,871
- NormedFieldstatement · cited by 1,084
- SeminormFamilystatement · cited by 68
Cited by74
Results whose statement or proof uses this declaration.
- norm_withSeminormsstatement · cited by 12
- WithSeminorms.topologicalAddGroupstatement and proof · cited by 11
- SeminormFamily.withSeminorms_iff_nhds_eq_iInfstatement and proof · cited by 8
- PolynormableSpace.withSeminormsstatement · cited by 6
- WithSeminorms.continuous_seminormstatement and proof · cited by 5
- WithSeminorms.hasBasisstatement and proof · cited by 5
- WithSeminorms.topology_eq_withSeminormsstatement and proof · cited by 5
- LinearMap.withSeminorms_inducedstatement and proof · cited by 5
- WithSeminorms.congr_equivstatement and proof · cited by 4
- WithSeminorms.continuous_normedSpace_rngstatement and proof · cited by 4
- WithSeminorms.continuous_of_isBoundedstatement and proof · cited by 4
- WithSeminorms.isVonNBounded_iff_seminorm_boundedstatement and proof · cited by 4