Theorems · Theorem · general topology
noncompactSpace_of_neBot
∀ {X : Type u} [inst : TopologicalSpace X], (Filter.cocompact X).NeBot → NoncompactSpace X- Defined in
- Mathlib.Topology.Compactness.Compact
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 87 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.
Cites10
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
- Set.univproof · cited by 3,945
- IsCompactproof · cited by 1,282
- Filter.NeBotstatement and proof · cited by 853
- Filter.cocompactstatement and proof · cited by 141
- Set.Nonempty.ne_emptyproof · cited by 65
- Set.compl_univproof · cited by 41
- Filter.nonempty_of_memproof · cited by 36
- NoncompactSpacestatement · cited by 21
- IsCompact.compl_mem_cocompactproof · cited by 13
Cited by2
Results whose statement or proof uses this declaration.
- Topology.IsClosedEmbedding.noncompactSpaceproof · cited by 1
- Filter.cocompact_neBot_iffproof · cited by 0