Theorems · Theorem · general topology
finite_of_compact_of_discrete
∀ {X : Type u} [inst : TopologicalSpace X] [CompactSpace X] [DiscreteTopology X], Finite XA compact discrete space is finite.
- Defined in
- Mathlib.Topology.Compactness.Compact
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 82 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.
- TopologicalSpacestatement and proof · cited by 24,529
- Finitestatement · cited by 3,029
- CompactSpacestatement and proof · cited by 593
- DiscreteTopologystatement and proof · cited by 373
- isCompact_univproof · cited by 53
- IsCompact.finite_of_discreteproof · cited by 4
- Finite.of_finite_univproof · cited by 4
Cited by6
Results whose statement or proof uses this declaration.
- IsCompact.finiteproof · cited by 5
- PrimeSpectrum.discreteTopology_iff_finite_and_krullDimLE_zeroproof · cited by 3
- Algebra.QuasiFinite.finite_comap_preimage_singletonproof · cited by 3
- AddSubgroup.quotient_finite_of_isOpenproof · cited by 2
- Subgroup.quotient_finite_of_isOpenproof · cited by 1
- DivisionRing.finite_of_compactSpace_of_t2Spaceproof · cited by 0