Theorems · Theorem · general topology
IsLindelof.of_isClosed_subset
∀ {X : Type u} [inst : TopologicalSpace X] {s t : Set X}, IsLindelof s → IsClosed t → t ⊆ s → IsLindelof tA closed subset of a Lindelöf set is a Lindelöf set.
- Defined in
- Mathlib.Topology.Compactness.Lindelof
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 77 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.
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
- IsClosedstatement and proof · cited by 1,639
- IsLindelofstatement and proof · cited by 85
- Set.inter_eq_self_of_subset_rightproof · cited by 39
- IsLindelof.inter_rightproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- IsClosed.isLindelofproof · cited by 2