Theorems · Theorem · general topology
isCompact_iff_isSeqCompact
∀ {X : Type u_1} [inst : TopologicalSpace X] [TopologicalSpace.PseudoMetrizableSpace X] {s : Set X},
IsCompact s ↔ IsSeqCompact sA version of Bolzano-Weierstrass: in a (pseudo)metrizable space, a set is compact if and only if it is sequentially compact.
- Defined in
- Mathlib.Topology.Sequences
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound
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- Setstatement and proof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- IsCompactstatement and proof · cited by 1,282
- TopologicalSpace.PseudoMetrizableSpacestatement and proof · cited by 245
- IsSeqCompactstatement and proof · cited by 26
- IsCompact.isSeqCompactproof · cited by 6
- IsSeqCompact.isCompactproof · cited by 1
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