Theorems · Theorem · general topology

IsSeqCompact.exists_tendsto

∀ {X : Type u_1} [inst : UniformSpace X] {s : Set X},
  IsSeqCompact s → ∀ {u : ℕ → X}, (∀ (n : ℕ), u n ∈ s) → CauchySeq u → ∃ x ∈ s, Filter.Tendsto u Filter.atTop (nhds x)

Defined in

Mathlib.Topology.Sequences

Cited by

1 results in Mathlib

Foundations

Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

UniformSpace