Theorems · Definition · general topology
Filter.coclosedCompact
(X : Type u_1) → [TopologicalSpace X] → Filter X
Filter.coclosedCompact is the filter generated by complements to closed compact sets.
In a Hausdorff space, this is the same as Filter.cocompact.
- Defined in
- Mathlib.Topology.Defs.Filter
- Cited by
- 20 results in Mathlib
- Foundations
- Depth 50 from the axioms · uses propext, 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.
- Setproof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Filterstatement · cited by 8,121
- Compl.complproof · cited by 2,925
- iInfproof · cited by 1,690
- IsClosedproof · cited by 1,639
- IsCompactproof · cited by 1,282
- Filter.principalproof · cited by 740
Cited by23
Results whose statement or proof uses this declaration.
- Filter.hasBasis_coclosedCompactstatement · cited by 8
- hasCompactSupport_iff_eventuallyEqstatement · cited by 7
- Filter.coclosedCompact_eq_cocompactstatement · cited by 5
- OnePoint.nhds_infty_eqstatement · cited by 4
- Filter.mem_coclosedCompact_iffstatement · cited by 3
- Bornology.relativelyCompactproof · cited by 3
- Filter.compl_mem_coclosedCompactstatement · cited by 2
- OnePoint.equivOfIsEmbeddingOfRangeEqproof · cited by 2
- OnePoint.tendsto_nhds_infty'statement and proof · cited by 2
- OnePoint.comap_coe_nhds_inftystatement and proof · cited by 1
- OnePoint.continuousAt_infty'statement · cited by 1
- OnePoint.continuous_map_iffstatement and proof · cited by 1