Theorems · Theorem · functional analysis

ContinuousLinearEquiv.isUniformEmbedding

∀ {R₁ : Type u_1} {R₂ : Type u_2} [inst : Semiring R₁] [inst_1 : Semiring R₂] {σ₁₂ : R₁ →+* R₂} {σ₂₁ : R₂ →+* R₁}
  [inst_2 : RingHomInvPair σ₁₂ σ₂₁] [inst_3 : RingHomInvPair σ₂₁ σ₁₂] {E₁ : Type u_8} {E₂ : Type u_9}
  [inst_4 : UniformSpace E₁] [inst_5 : UniformSpace E₂] [inst_6 : AddCommGroup E₁] [inst_7 : AddCommGroup E₂]
  [inst_8 : Module R₁ E₁] [inst_9 : Module R₂ E₂] [IsUniformAddGroup E₁] [IsUniformAddGroup E₂] (e : E₁ ≃SL[σ₁₂] E₂),
  IsUniformEmbedding ⇑e

Defined in

Mathlib.Topology.Algebra.Module.Equiv

Cited by

4 results in Mathlib

Foundations

Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringSemiringRingHomInvPairRingHomInvPairUniformSpaceUniformSpaceAddCommGroupAddCommGroupModuleModuleIsUniformAddGroupIsUniformAddGroup