Theorems · Theorem · general topology
Filter.cocompact_eq_cofinite
∀ (X : Type u_2) [inst : TopologicalSpace X] [DiscreteTopology X], Filter.cocompact X = Filter.cofinite
- Defined in
- Mathlib.Topology.Compactness.Compact
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Filterstatement · cited by 8,121
- Compl.complproof · cited by 2,925
- Set.Finiteproof · cited by 1,814
- iInfproof · cited by 1,690
- Filter.principalproof · cited by 740
- DiscreteTopologystatement and proof · cited by 373
- Filter.cofinitestatement · cited by 251
- iInf_congr_Propproof · cited by 218
- Filter.cocompactstatement · cited by 141
- Filter.HasBasis.eq_biInfproof · cited by 15
Cited by7
Results whose statement or proof uses this declaration.
- Int.cofinite_eqproof · cited by 7
- tendsto_norm_comp_cofinite_atTop_of_isClosedEmbeddingproof · cited by 3
- tendsto_cofinite_cocompact_of_discreteproof · cited by 1
- Filter.Tendsto.isCompact_insert_range_of_cofiniteproof · cited by 1
- OnePoint.continuous_iff_from_discreteproof · cited by 1
- tendsto_mul_cofinite_nhds_zeroproof · cited by 1
- tendsto_norm_comp_cofinite_atTop_of_isClosedEmbedding'proof · cited by 0