Theorems · Theorem · general topology
IsCompact.union
∀ {X : Type u} [inst : TopologicalSpace X] {s t : Set X}, IsCompact s → IsCompact t → IsCompact (s ∪ t)- Defined in
- Mathlib.Topology.Compactness.Compact
- Cited by
- 23 results in Mathlib
- Foundations
- Depth 84 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.
Cites5
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
- IsCompactstatement and proof · cited by 1,282
- Set.union_eq_iUnionproof · cited by 28
- isCompact_iUnionproof · cited by 6
Cited by23
Results whose statement or proof uses this declaration.
- Filter.hasBasis_cocompactproof · cited by 14
- Filter.hasBasis_coclosedCompactproof · cited by 8
- IsCompact.insertproof · cited by 3
- GromovHausdorff.ghDist_le_hausdorffDistproof · cited by 3
- MeasureTheory.measure_univ_of_isAddLeftInvariantproof · cited by 2
- CompactlySupportedContinuousMap.exists_add_of_leproof · cited by 2
- Filter.HasBasis.compactConvergenceUniformityproof · cited by 2
- IsRetrocompact.unionproof · cited by 2
- dist_integral_mulExpNegMulSq_comp_leproof · cited by 1
- MeasureTheory.measure_univ_of_isMulLeftInvariantproof · cited by 1
- AlgebraicGeometry.quasiSeparatedSpace_iff_forall_affineOpensproof · cited by 1
- MeasureTheory.Measure.haar.index_union_eqproof · cited by 1