Theorems · Theorem · general topology
isCompact_iff_isCompact_univ
∀ {X : Type u} [inst : TopologicalSpace X] {s : Set X}, IsCompact s ↔ IsCompact Set.univ- Defined in
- Mathlib.Topology.Compactness.Compact
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 79 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.
Cites8
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
- Set.Elemstatement · cited by 7,166
- Set.univstatement · cited by 3,945
- IsCompactstatement and proof · cited by 1,282
- Set.image_univproof · cited by 322
- Subtype.range_coeproof · cited by 98
- Subtype.isCompact_iffproof · cited by 1
Cited by5
Results whose statement or proof uses this declaration.
- isCompact_iff_compactSpaceproof · cited by 50
- GromovHausdorff.ghDist_le_hausdorffDistproof · cited by 3
- ContinuousMap.compactOpen_eq_iInf_inducedproof · cited by 2
- summableLocallyUniformlyOn_iteratedDerivWithin_smul_cexpproof · cited by 2
- IsCompact.elim_finite_subfamily_isClosed_subtypeproof · cited by 1