Theorems · Theorem · general topology
IsCompact.compl_mem_cocompact
∀ {X : Type u} [inst : TopologicalSpace X] {s : Set X}, IsCompact s → sᶜ ∈ Filter.cocompact X- Defined in
- Mathlib.Topology.Compactness.Compact
- Cited by
- 13 results in Mathlib
- Foundations
- Depth 86 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
- Filterstatement · cited by 8,121
- Compl.complstatement · cited by 2,925
- IsCompactstatement and proof · cited by 1,282
- Filter.cocompactstatement · cited by 141
- Filter.HasBasis.mem_of_memproof · cited by 63
- Filter.hasBasis_cocompactproof · cited by 14
Cited by13
Results whose statement or proof uses this declaration.
- Topology.IsClosedEmbedding.tendsto_cocompactproof · cited by 9
- Metric.cobounded_eq_cocompactproof · cited by 8
- isProperMap_iff_tendsto_cocompactproof · cited by 2
- noncompactSpace_of_neBotproof · cited by 2
- Filter.coprod_cocompactproof · cited by 1
- Rat.not_countably_generated_cocompactproof · cited by 1
- Filter.cocompact_le_cofiniteproof · cited by 1
- isProperMap_iff_isClosedMap_and_tendsto_cofiniteproof · cited by 1
- AddSubgroup.properlyDiscontinuousVAdd_of_tendsto_cofiniteproof · cited by 0
- AddSubgroup.properlyDiscontinuousVAdd_opposite_of_tendsto_cofiniteproof · cited by 0
- disjoint_nhds_cocompactproof · cited by 0
- Subgroup.properlyDiscontinuousSMul_of_tendsto_cofiniteproof · cited by 0