Theorems · Theorem · functional analysis

isClosedEmbedding_smul_left

∀ {𝕜 : Type u_1} {E : Type u_2} [inst : NontriviallyNormedField 𝕜] [CompleteSpace 𝕜] [inst_2 : AddCommGroup E]
  [inst_3 : TopologicalSpace E] [IsTopologicalAddGroup E] [inst_5 : Module 𝕜 E] [ContinuousSMul 𝕜 E] [T2Space E]
  {c : E}, c ≠ 0 → Topology.IsClosedEmbedding fun x => x • c

Defined in

Mathlib.Topology.Algebra.Module.FiniteDimension

Cited by

5 results in Mathlib

Foundations

Depth 175 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldCompleteSpaceAddCommGroupTopologicalSpaceIsTopologicalAddGroupModuleContinuousSMulT2Space