Theorems · Theorem · functional analysis

Euclidean.exists_pos_lt_subset_ball

∀ {E : Type u_1} [inst : AddCommGroup E] [inst_1 : TopologicalSpace E] [inst_2 : IsTopologicalAddGroup E]
  [inst_3 : T2Space E] [inst_4 : Module ℝ E] [inst_5 : ContinuousSMul ℝ E] [inst_6 : FiniteDimensional ℝ E] {R : ℝ}
  {s : Set E} {x : E}, 0 < R → IsClosed s → s ⊆ Euclidean.ball x R → ∃ r ∈ Set.Ioo 0 R, s ⊆ Euclidean.ball x r

Defined in

Mathlib.Analysis.InnerProductSpace.EuclideanDist

Cited by

0 results in Mathlib

Foundations

Depth 229 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommGroupTopologicalSpaceIsTopologicalAddGroupT2SpaceModuleContinuousSMulFiniteDimensional