Theorems · Theorem · general topology
SeqCompactSpace.tendsto_subseq
∀ {X : Type u_1} [inst : TopologicalSpace X] [SeqCompactSpace X] (x : ℕ → X),
∃ a φ, StrictMono φ ∧ Filter.Tendsto (x ∘ φ) Filter.atTop (nhds a)- Defined in
- Mathlib.Topology.Sequences
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 23 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement and proof · cited by 24,529
- nhdsstatement and proof · cited by 5,554
- Set.univproof · cited by 3,945
- Filter.Tendstostatement and proof · cited by 3,814
- Filter.atTopstatement and proof · cited by 2,405
- StrictMonostatement and proof · cited by 706
- Set.mem_univproof · cited by 416
- SeqCompactSpacestatement and proof · cited by 7
- SeqCompactSpace.isSeqCompact_univproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- CompactSpace.tendsto_subseqproof · cited by 0