Theorems · Theorem · Lie groups

totallyBounded_iff_subset_finite_iUnion_nhds_zero

∀ {α : Type u_1} [inst : UniformSpace α] [inst_1 : AddGroup α] [IsUniformAddGroup α] {s : Set α},
  TotallyBounded s ↔ ∀ U ∈ nhds 0, ∃ t, t.Finite ∧ s ⊆ ⋃ y ∈ t, y +ᵥ U

Defined in

Mathlib.Topology.Algebra.IsUniformGroup.Basic

Cited by

4 results in Mathlib

Foundations

Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

UniformSpaceAddGroupIsUniformAddGroup