Theorems · Theorem · general topology
not_compactSpace_iff
∀ {X : Type u} [inst : TopologicalSpace X], ¬CompactSpace X ↔ NoncompactSpace X- Defined in
- Mathlib.Topology.Compactness.Compact
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 54 from the axioms · uses propext, Quot.sound
- Assumes
- TopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- CompactSpacestatement and proof · cited by 593
- NoncompactSpacestatement and proof · cited by 21
Cited by1
Results whose statement or proof uses this declaration.
- Metric.ediam_univ_eq_top_iff_noncompactproof · cited by 1