Theorems · Theorem · general topology
IsSeqCompact.isCompact
∀ {X : Type u_1} [inst : TopologicalSpace X] [TopologicalSpace.PseudoMetrizableSpace X] {s : Set X},
IsSeqCompact s → IsCompact sIn a (pseudo)metrizable space, any sequentially compact set is compact.
- Defined in
- Mathlib.Topology.Sequences
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- IsCompactstatement · cited by 1,282
- TopologicalSpace.PseudoMetrizableSpacestatement and proof · cited by 245
- IsSeqCompactstatement and proof · cited by 26
- isCompact_iff_totallyBounded_isCompleteproof · cited by 6
- IsSeqCompact.isCompleteproof · cited by 1
- IsSeqCompact.totallyBoundedproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- isCompact_iff_isSeqCompactproof · cited by 0