Theorems · Theorem · general topology
Set.Finite.isCompact
∀ {X : Type u} [inst : TopologicalSpace X] {s : Set X}, s.Finite → IsCompact s- Defined in
- Mathlib.Topology.Compactness.Compact
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- Set.Finitestatement and proof · cited by 1,814
- IsCompactstatement · cited by 1,282
- Set.biUnion_of_singletonproof · cited by 43
- isCompact_singletonproof · cited by 32
- Set.Finite.isCompact_biUnionproof · cited by 11
Cited by10
Results whose statement or proof uses this declaration.
- TopologicalSpace.Compacts.closure_finite_subsetsproof · cited by 3
- ZLattice.exists_finsetSum_norm_rpow_le_tsumproof · cited by 2
- isCompact_iff_finiteproof · cited by 2
- SeparatedNhds.of_finset_finsetproof · cited by 2
- TopologicalSpace.Compacts.isPreconnected_nonempty_finite_subsetsproof · cited by 2
- HasCompactSupport.zeroproof · cited by 1
- Filter.cocompact_le_cofiniteproof · cited by 1
- isCountablyCompact_iff_infinite_subset_has_accPtproof · cited by 0
- Metric.isCompact_closure_iff_exists_finite_isCoverproof · cited by 0