Theorems · Theorem · functional analysis
WithSeminorms.topologicalAddGroup
∀ {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 : TopologicalSpace E] {p : SeminormFamily 𝕜 E ι}, WithSeminorms p → IsTopologicalAddGroup E- Cited by
- 11 results in Mathlib
- Foundations
- Depth 135 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- IsTopologicalAddGroupstatement and proof · cited by 1,394
- NormedFieldstatement and proof · cited by 1,084
- WithSeminormsstatement and proof · cited by 69
- SeminormFamilystatement and proof · cited by 68
- SeminormFamily.moduleFilterBasisproof · cited by 10
- ModuleFilterBasis.toAddGroupFilterBasisproof · cited by 10
- WithSeminorms.withSeminorms_eqproof · cited by 2
Cited by11
Results whose statement or proof uses this declaration.
- WithSeminorms.continuous_seminormproof · cited by 5
- LinearMap.withSeminorms_inducedproof · cited by 5
- WithSeminorms.continuous_of_isBoundedproof · cited by 4
- WithSeminorms.continuous_of_continuous_compproof · cited by 3
- withSeminorms_iInfproof · cited by 3
- WithSeminorms.toPolynormableSpaceproof · cited by 3
- WithSeminorms.hasBasis_ballproof · cited by 2
- Seminorm.exists_le_comp_of_isInducingproof · cited by 1
- WithSeminorms.T1_of_separatingproof · cited by 1
- WithSeminorms.toLocallyConvexSpaceproof · cited by 1
- WithSeminorms.firstCountableTopologyproof · cited by 0