Theorems · Theorem · general topology
IsCompact.insert
∀ {X : Type u} [inst : TopologicalSpace X] {s : Set X}, IsCompact s → ∀ (a : X), IsCompact (insert a s)- Defined in
- Mathlib.Topology.Compactness.Compact
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 85 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.
Cites5
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 and proof · cited by 1,282
- isCompact_singletonproof · cited by 32
- IsCompact.unionproof · cited by 23
Cited by3
Results whose statement or proof uses this declaration.
- isCompact_range_of_support_subset_isCompactproof · cited by 2
- ContinuousOn.exists_isMinOn'proof · cited by 2
- isCompact_range_of_mulSupport_subset_isCompactproof · cited by 2