Theorems · Theorem · general topology
IsCompact.isSeqCompact
∀ {X : Type u_1} [inst : TopologicalSpace X] [FirstCountableTopology X] {s : Set X}, IsCompact s → IsSeqCompact s- Defined in
- Mathlib.Topology.Sequences
- Cited by
- 6 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.
Cites14
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
- nhdsproof · cited by 5,554
- Filter.Tendstoproof · cited by 3,814
- Filter.atTopproof · cited by 2,405
- IsCompactstatement and proof · cited by 1,282
- Filter.mapproof · cited by 819
- StrictMonoproof · cited by 706
- Filter.Eventually.of_forallproof · cited by 526
- ClusterPtproof · cited by 138
- FirstCountableTopologystatement and proof · cited by 106
- Filter.tendsto_principalproof · cited by 28
Cited by6
Results whose statement or proof uses this declaration.
- upperHemicontinuous_spectrumproof · cited by 4
- IsCompact.tendsto_subseqproof · cited by 4
- MeasureTheory.exists_measure_iUnion_gt_of_isCompact_closureproof · cited by 1
- tendsto_subseq_of_frequently_boundedproof · cited by 1
- isCompact_iff_isSeqCompactproof · cited by 0
- IsCompact.tendsto_subseq'proof · cited by 0