Theorems · Theorem · general topology
Set.Subsingleton.isCompact
∀ {X : Type u} [inst : TopologicalSpace X] {s : Set X}, s.Subsingleton → IsCompact s- Defined in
- Mathlib.Topology.Compactness.Compact
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 62 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.
Cites7
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
- IsCompactstatement · cited by 1,282
- Set.Subsingletonstatement and proof · cited by 276
- isCompact_singletonproof · cited by 32
- isCompact_emptyproof · cited by 17
- Set.Subsingleton.induction_onproof · cited by 12
Cited by2
Results whose statement or proof uses this declaration.
- isProperMap_iff_isClosedMap_of_injproof · cited by 1
- IsRetrocompact.singletonproof · cited by 0