Theorems · Theorem · general topology

Filter.totallyBounded_biSup

∀ {α : Type u} [uniformSpace : UniformSpace α] {ι : Type u_1} {I : Set ι},
  I.Finite → ∀ {f : ι → Filter α}, (⨆ i ∈ I, f i).TotallyBounded ↔ ∀ i ∈ I, (f i).TotallyBounded

Defined in

Mathlib.Topology.UniformSpace.Cauchy

Cited by

1 results in Mathlib

Foundations

Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

UniformSpace