Theorems · Theorem · general topology
IsSeqCompact.subseq_of_frequently_in
∀ {X : Type u_1} [inst : TopologicalSpace X] {s : Set X},
IsSeqCompact s →
∀ {x : ℕ → X},
(∃ᶠ (n : ℕ) in Filter.atTop, x n ∈ s) → ∃ a ∈ s, ∃ φ, StrictMono φ ∧ Filter.Tendsto (x ∘ φ) Filter.atTop (nhds a)- Defined in
- Mathlib.Topology.Sequences
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- nhdsstatement and proof · cited by 5,554
- Filter.Tendstostatement and proof · cited by 3,814
- Filter.atTopstatement and proof · cited by 2,405
- StrictMonostatement and proof · cited by 706
- Filter.Frequentlystatement and proof · cited by 414
- StrictMono.compproof · cited by 36
- IsSeqCompactstatement and proof · cited by 26
- Filter.extraction_of_frequently_atTopproof · cited by 5
Cited by5
Results whose statement or proof uses this declaration.
- UpperHemicontinuousAt.of_sequencesproof · cited by 1
- IsSeqCompact.exists_tendsto_of_frequently_memproof · cited by 1
- tendsto_subseq_of_frequently_boundedproof · cited by 1
- IsSeqCompact.isCountablyCompactproof · cited by 1
- IsCompact.tendsto_subseq'proof · cited by 0