Theorems · Theorem · functional analysis
WithSeminorms.topology_eq_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]
{p : SeminormFamily 𝕜 E ι} [topology : TopologicalSpace E], WithSeminorms p → topology = p.moduleFilterBasis.topology- Cited by
- 5 results in Mathlib
- Foundations
- Depth 133 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- NormedFieldstatement and proof · cited by 1,084
- WithSeminormsstatement and proof · cited by 69
- SeminormFamilystatement and proof · cited by 68
- SeminormFamily.moduleFilterBasisstatement · cited by 10
- ModuleFilterBasis.topologystatement · cited by 3
Cited by5
Results whose statement or proof uses this declaration.
- SeminormFamily.withSeminorms_iff_nhds_eq_iInfproof · cited by 8
- WithSeminorms.hasBasisproof · cited by 5
- WithSeminorms.congrproof · cited by 3
- WithSeminorms.withSeminorms_eqproof · cited by 2
- WithSeminorms.toLocallyConvexSpaceproof · cited by 1