Theorems · Theorem · general topology
NoncompactSpace.noncompact_univ
∀ {X : Type u_1} {inst : TopologicalSpace X} [self : NoncompactSpace X], ¬IsCompact Set.univIn a noncompact space, Set.univ is not a compact set.
- Defined in
- Mathlib.Topology.Defs.Filter
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 50 from the axioms · uses propext, Quot.sound
- Assumes
- NoncompactSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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.univstatement · cited by 3,945
- IsCompactstatement · cited by 1,282
- NoncompactSpacestatement and proof · cited by 21
Cited by1
Results whose statement or proof uses this declaration.
- noncompact_univproof · cited by 1