Theorems · Theorem · general topology
TopologicalSpace.Compacts.isCompact
∀ {α : Type u_1} [inst : TopologicalSpace α] (s : TopologicalSpace.Compacts α), IsCompact ↑s- Defined in
- Mathlib.Topology.Sets.Compacts
- Cited by
- 18 results in Mathlib
- Foundations
- Depth 55 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
- SetLike.coestatement · cited by 8,199
- IsCompactstatement · cited by 1,282
- TopologicalSpace.Compactsstatement and proof · cited by 386
- TopologicalSpace.Compacts.isCompact'proof · cited by 19
Cited by18
Results whose statement or proof uses this declaration.
- ContDiffMapSupportedIn.hasCompactSupportproof · cited by 4
- MeasureTheory.Content.innerContent_iSup_natproof · cited by 3
- TopologicalSpace.Compacts.isOpen_setOfPred_disjoint_coeproof · cited by 3
- TopologicalSpace.Compacts.continuous_prodproof · cited by 2
- TopologicalSpace.Compacts.isCompact_biUnion_coe_of_isCompactproof · cited by 2
- TopologicalSpace.IsTopologicalBasis.compactsproof · cited by 2
- TopologicalSpace.Compacts.range_mapproof · cited by 2
- MeasureTheory.Content.borel_le_caratheodoryproof · cited by 1
- TopologicalSpace.Compacts.isClosedEmbedding_toClosedsproof · cited by 1
- MeasureTheory.Measure.haar.is_left_invariant_addPrehaarproof · cited by 1
- MeasureTheory.Measure.haar.is_left_invariant_prehaarproof · cited by 1
- MeasureTheory.Measure.haar.le_addIndex_mulproof · cited by 1