Theorems · Inductive type · general topology
SeqCompactSpace
(X : Type u_1) → [TopologicalSpace X] → Prop
A space X is sequentially compact if every sequence in X has a
converging subsequence.
- Defined in
- Mathlib.Topology.Defs.Sequences
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 1 from the axioms · uses no axioms
- Assumes
- TopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement · cited by 24,529
Cited by9
Results whose statement or proof uses this declaration.
- SeqCompactSpace.isSeqCompact_univstatement and proof · cited by 3
- isSeqCompact_iff_seqCompactSpacestatement · cited by 1
- isSeqCompact_univ_iffstatement and proof · cited by 1
- SeqCompactSpace.casesOnstatement and proof · cited by 1
- IsSeqCompact.rangestatement and proof · cited by 1
- SeqCompactSpace.tendsto_subseqstatement and proof · cited by 1
- compactSpace_iff_seqCompactSpacestatement · cited by 0
- SeqCompactSpace.recOnstatement and proof · cited by 0
- seqCompactSpace_iffstatement and proof · cited by 0