Theorems · Theorem · general topology
isCompact_iff_finite
∀ {X : Type u} [inst : TopologicalSpace X] {s : Set X} [DiscreteTopology X], IsCompact s ↔ s.Finite- Defined in
- Mathlib.Topology.Compactness.Compact
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound
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 and proof · cited by 1,282
- DiscreteTopologystatement and proof · cited by 373
- Set.Finite.isCompactproof · cited by 10
- IsCompact.finite_of_discreteproof · cited by 4
Cited by2
Results whose statement or proof uses this declaration.
- PeriodPair.hasSumLocallyUniformly_auxproof · cited by 2
- properlyDiscontinuousVAdd_iff_properVAddproof · cited by 0