Theorems · Theorem · general topology

IsCompact.tendsto_subseq

∀ {X : Type u_1} [inst : TopologicalSpace X] [FirstCountableTopology X] {s : Set X} {x : ℕ → X},
  IsCompact s → (∀ (n : ℕ), x n ∈ s) → ∃ a ∈ s, ∃ φ, StrictMono φ ∧ Filter.Tendsto (x ∘ φ) Filter.atTop (nhds a)

Defined in

Mathlib.Topology.Sequences

Cited by

4 results in Mathlib

Foundations

Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceFirstCountableTopology