Theorems · Theorem · general topology
isCompact_univ_iff
∀ {X : Type u} [inst : TopologicalSpace X], IsCompact Set.univ ↔ CompactSpace X- Defined in
- Mathlib.Topology.Compactness.Compact
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 51 from the axioms · uses propext, 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.
- TopologicalSpacestatement and proof · cited by 24,529
- Set.univstatement and proof · cited by 3,945
- IsCompactstatement and proof · cited by 1,282
- CompactSpacestatement and proof · cited by 593
- CompactSpace.isCompact_univproof · cited by 14
Cited by9
Results whose statement or proof uses this declaration.
- isCompact_iff_compactSpaceproof · cited by 50
- AlgebraicGeometry.isAffine_of_isAffineOpen_basicOpenproof · cited by 2
- summableLocallyUniformlyOn_iteratedDerivWithin_smul_cexpproof · cited by 2
- compactSpace_generateFromproof · cited by 1
- ArzelaAscoli.compactSpace_of_closed_inducing'proof · cited by 1
- compactSpace_generateFrom'proof · cited by 0
- AlgebraicGeometry.Scheme.quasiSeparatedSpace_of_isOpenCoverproof · cited by 0
- AlgebraicGeometry.Scheme.OpenCover.compactSpaceproof · cited by 0