Theorems · Theorem · general topology

Metric.PiNatEmbed.separation

∀ {X : Type u_3} [inst : MetricSpace X] [inst_1 : TopologicalSpace.SeparableSpace X] {x : X} {C : Set X},
  C ∈ nhds x → ∃ n, C ∈ Filter.comap (Metric.PiNatEmbed.distDenseSeq X n) (nhds (Metric.PiNatEmbed.distDenseSeq X n x))

Defined in

Mathlib.Topology.MetricSpace.PiNat

Cited by

2 results in Mathlib

Foundations

Depth 156 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MetricSpaceTopologicalSpace.SeparableSpace