Theorems · Theorem · general topology
Filter.hasBasis_coclosedCompact
∀ {X : Type u} [inst : TopologicalSpace X],
(Filter.coclosedCompact X).HasBasis (fun s => IsClosed s ∧ IsCompact s) compl- Defined in
- Mathlib.Topology.Compactness.Compact
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 85 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.
Cites17
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
- Compl.complstatement and proof · cited by 2,925
- iInfproof · cited by 1,690
- IsClosedstatement and proof · cited by 1,639
- IsCompactstatement and proof · cited by 1,282
- Filter.HasBasisstatement and proof · cited by 604
- Set.subset_union_leftproof · cited by 142
- Set.subset_union_rightproof · cited by 123
- Set.compl_subset_complproof · cited by 50
- isClosed_emptyproof · cited by 26
- IsCompact.unionproof · cited by 23
Cited by8
Results whose statement or proof uses this declaration.
- Filter.coclosedCompact_eq_cocompactproof · cited by 5
- Filter.mem_coclosedCompact_iffproof · cited by 3
- OnePoint.nhdsNE_infty_eqproof · cited by 1
- Homeomorph.comap_coclosedCompactproof · cited by 1
- OnePoint.hasBasis_nhds_inftyproof · cited by 1
- OnePoint.continuousAt_inftyproof · cited by 0
- IsCompact.compl_mem_coclosedCompact_of_isClosedproof · cited by 0
- OnePoint.tendsto_nhds_inftyproof · cited by 0