Theorems · Theorem · general topology
IsCompact.finite_of_discrete
∀ {X : Type u} [inst : TopologicalSpace X] {s : Set X} [DiscreteTopology X], IsCompact s → s.Finite- Defined in
- Mathlib.Topology.Compactness.Compact
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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
- Finsetproof · cited by 13,712
- SetLike.coeproof · cited by 8,199
- nhdsproof · cited by 5,554
- Set.iUnionproof · cited by 2,483
- Set.Finitestatement · cited by 1,814
- IsCompactstatement and proof · cited by 1,282
- DiscreteTopologystatement and proof · cited by 373
- Set.Finite.subsetproof · cited by 285
- Finset.finite_toSetproof · cited by 210
- Set.biUnion_of_singletonproof · cited by 43
Cited by4
Results whose statement or proof uses this declaration.
- finite_of_compact_of_discreteproof · cited by 6
- isCompact_iff_finiteproof · cited by 2
- IsLocallyConstant.range_finiteproof · cited by 1
- TopologicalSpace.NoetherianSpace.finiteproof · cited by 0