Theorems · Theorem · general topology

cauchy_map_iff_exists_tendsto

∀ {α : Type u} {β : Type v} [uniformSpace : UniformSpace α] [CompleteSpace α] {l : Filter β} {f : β → α} [l.NeBot],
  Cauchy (Filter.map f l) ↔ ∃ x, Filter.Tendsto f l (nhds x)

Defined in

Mathlib.Topology.UniformSpace.Cauchy

Cited by

4 results in Mathlib

Foundations

Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

UniformSpaceCompleteSpaceFilter.NeBot