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Theorems · Definition · functional analysis

SeminormedRing.induced

{F : Type u_5} →
  (R : Type u_6) →
    (S : Type u_7) →
      [inst : FunLike F R S] →
        [inst_1 : Ring R] → [inst_2 : SeminormedRing S] → [NonUnitalRingHomClass F R S] → F → SeminormedRing R

A non-unital ring homomorphism from a Ring to a SeminormedRing induces a SeminormedRing structure on the domain. See note [reducible non-instances]

Defined in
Mathlib.Analysis.Normed.Ring.Basic
Cited by
2 results in Mathlib
Foundations
Depth 124 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
FunLikeRingSeminormedRingNonUnitalRingHomClass
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Around this declaration

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

NormMulClass.induced · cited by 0NormMulClass.inducedNormedAlgebra.induced · cited by 0NormedAlgebra.inducedNormOneClass.induced · cited by 0NormOneClass.inducedEquiv.seminormedRing · cited by 0Equiv.seminormedRingRing · cited by 7463RingFunLike · cited by 2560FunLikeSeminormedRing · cited by 446SeminormedRingNonUnitalRingHomClass · cited by 82NonUnitalRingHomClassSeminormedRing.inducedCITED BYCITES

Cites4

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Cited by4

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