Theorems · Theorem · general topology

UniformSpace.subset_countable_closure_of_almost_dense_set

∀ {α : Type u} [uniformSpace : UniformSpace α] [(uniformity α).IsCountablyGenerated] (s : Set α),
  (∀ U ∈ uniformity α, ∃ t, t.Countable ∧ s ⊆ ⋃ x ∈ t, UniformSpace.ball x U) → ∃ t ⊆ s, t.Countable ∧ s ⊆ closure t

Defined in

Mathlib.Topology.UniformSpace.Cauchy

Cited by

4 results in Mathlib

Foundations

Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

UniformSpaceFilter.IsCountablyGenerated