Mathlib Map

Theorems Β· Definition Β· functional analysis

SeminormFamily.comp

{π•œ : Type u_2} β†’
  {π•œβ‚‚ : Type u_3} β†’
    {E : Type u_6} β†’
      {F : Type u_7} β†’
        {ΞΉ : Type u_9} β†’
          [inst : NormedField π•œ] β†’
            [inst_1 : AddCommGroup E] β†’
              [inst_2 : Module π•œ E] β†’
                [inst_3 : NormedField π•œβ‚‚] β†’
                  [inst_4 : AddCommGroup F] β†’
                    [inst_5 : Module π•œβ‚‚ F] β†’
                      {σ₁₂ : π•œ β†’+* π•œβ‚‚} β†’
                        [RingHomIsometric σ₁₂] β†’ SeminormFamily π•œβ‚‚ F ΞΉ β†’ (E β†’β‚›β‚—[σ₁₂] F) β†’ SeminormFamily π•œ E ΞΉ

The family of seminorms obtained by composing each seminorm by a linear map.

Defined in
Mathlib.Analysis.LocallyConvex.WithSeminorms
Cited by
8 results in Mathlib
Foundations
Depth 106 from the axioms Β· uses propext, Classical.choice, Quot.sound
Assumes
NormedFieldAddCommGroupModuleNormedFieldAddCommGroupModuleRingHomIsometric
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

LinearMap.withSeminorms_induced Β· cited by 5LinearMap.withSeminorms_i…Topology.IsInducing.withSeminorms Β· cited by 4IsInducing.withSeminormswithSeminorms_pi Β· cited by 3withSeminorms_piSeminorm.bound_comp_of_isInducing Β· cited by 1Seminorm.bound_comp_of_is…SeminormFamily.finset_sup_comp Β· cited by 1SeminormFamily.finset_sup…SeminormFamily.comp_apply Β· cited by 0SeminormFamily.comp_applySeminormFamily.comp_smul_nnreal Β· cited by 0SeminormFamily.comp_smul_…SeminormFamily.comp.congr_simp Β· cited by 0comp.congr_simpModule Β· cited by 20661ModuleAddCommGroup Β· cited by 12871AddCommGroupLinearMap Β· cited by 10215LinearMapRingHom Β· cited by 10189RingHomNormedField Β· cited by 1084NormedFieldRingHomIsometric Β· cited by 282RingHomIsometricSeminormFamily Β· cited by 68SeminormFamilySeminorm.comp Β· cited by 53Seminorm.compSeminormFamily.compCITED BYCITES

Cites8

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Cited by8

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