Theorems · Theorem · general topology
IsCompact.ne_univ
∀ {X : Type u} [inst : TopologicalSpace X] {s : Set X} [NoncompactSpace X], IsCompact s → s ≠ Set.univ- Defined in
- Mathlib.Topology.Compactness.Compact
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 52 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- Set.univstatement and proof · cited by 3,945
- IsCompactstatement and proof · cited by 1,282
- NoncompactSpacestatement and proof · cited by 21
- noncompact_univproof · cited by 1
Cited by4
Results whose statement or proof uses this declaration.
- Complex.exists_mem_frontier_isMaxOn_normproof · cited by 1
- exists_disjoint_smul_of_isCompactproof · cited by 1
- exists_disjoint_vadd_of_isCompactproof · cited by 1
- IsCompact.exists_mem_frontier_infDist_compl_eq_distproof · cited by 0