Theorems · Theorem · functional analysis

LinearMap.isInducing_of_restrict_nhds_zero

∀ {𝕜₁ : Type u_1} {𝕜₂ : Type u_2} {E : Type u_3} {F : Type u_4} [inst : NontriviallyNormedField 𝕜₁]
  [inst_1 : NontriviallyNormedField 𝕜₂] [inst_2 : AddCommGroup E] [inst_3 : AddCommGroup F] [inst_4 : Module 𝕜₁ E]
  [inst_5 : Module 𝕜₂ F] {σ : 𝕜₁ →+* 𝕜₂} {f : E →ₛₗ[σ] F} [inst_6 : TopologicalSpace E] [inst_7 : TopologicalSpace F]
  [IsTopologicalAddGroup E] [IsTopologicalAddGroup F] [ContinuousSMul 𝕜₁ E] [ContinuousSMul 𝕜₂ F] [RingHomIsometric σ]
  {V : Set E}, V ∈ nhds 0 → Topology.IsInducing (V.domRestrict ⇑f) → Topology.IsInducing ⇑f

Defined in

Mathlib.Topology.Algebra.Module.EmbeddingOfLocal

Cited by

1 results in Mathlib

Foundations

Depth 154 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNontriviallyNormedFieldAddCommGroupAddCommGroupModuleModuleTopologicalSpaceTopologicalSpaceIsTopologicalAddGroupIsTopologicalAddGroupContinuousSMulContinuousSMulRingHomIsometric