Theorems · Theorem · general topology
isCompact_univ
∀ {X : Type u} [inst : TopologicalSpace X] [h : CompactSpace X], IsCompact Set.univ- Defined in
- Mathlib.Topology.Compactness.Compact
- Cited by
- 53 results in Mathlib
- Foundations
- Depth 51 from the axioms · uses propext, Quot.sound
- Assumes
- TopologicalSpaceCompactSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- Set.univstatement · cited by 3,945
- IsCompactstatement · cited by 1,282
- CompactSpacestatement and proof · cited by 593
- CompactSpace.isCompact_univproof · cited by 14
Cited by53
Results whose statement or proof uses this declaration.
- IsClosed.isCompactproof · cited by 43
- isCompact_rangeproof · cited by 24
- finite_of_compact_of_discreteproof · cited by 6
- Filter.cocompact_eq_botproof · cited by 5
- Homeomorph.compactSpaceproof · cited by 4
- isCompact_setOfPred_finiteMeasure_le_of_compactSpaceproof · cited by 3
- HasCompactSupport.of_compactSpaceproof · cited by 3
- AlgebraicGeometry.Scheme.IsQuasiAffine.of_forall_exists_mem_basicOpenproof · cited by 2
- Topology.IsLocallyConstructible.isConstructibleproof · cited by 2
- continuous_ultrafilter_extendproof · cited by 2
- tendstoLocallyUniformly_iff_tendstoUniformly_of_compactSpaceproof · cited by 2
- Metric.isBounded_of_compactSpaceproof · cited by 2