Theorems · Theorem · general topology
CompactSpace.isCompact_univ
∀ {X : Type u_1} {inst : TopologicalSpace X} [self : CompactSpace X], IsCompact Set.univIn a compact space, Set.univ is a compact set.
- Defined in
- Mathlib.Topology.Defs.Filter
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 50 from the axioms · uses propext, Quot.sound
- Assumes
- CompactSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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
Cited by14
Results whose statement or proof uses this declaration.
- isCompact_univproof · cited by 53
- AlgebraicGeometry.IsAffineOpen.isCompactproof · cited by 17
- isCompact_univ_iffproof · cited by 9
- AlgebraicGeometry.QuasiCompact.compactSpace_of_compactSpaceproof · cited by 7
- CompactSpace.elim_nhds_subcoverproof · cited by 5
- IsRetrocompact.isCompactproof · cited by 2
- CompactSpace.iInter_nonemptyproof · cited by 1
- CategoryTheory.PreGaloisCategory.toAut_surjective_of_isPretransitiveproof · cited by 1
- AlgebraicGeometry.exists_of_res_zero_of_qcqs_of_topproof · cited by 1
- AlgebraicGeometry.Scheme.zeroLocus_eq_univ_iff_subset_nilradicalproof · cited by 0
- CompactSpace.nonempty_sInterproof · cited by 0
- AlgebraicGeometry.exists_of_res_eq_of_qcqs_of_topproof · cited by 0