Theorems · Theorem · general topology
countable_cover_nhds_interior
∀ {X : Type u} [inst : TopologicalSpace X] [LindelofSpace X] {U : X → Set X},
(∀ (x : X), U x ∈ nhds x) → ∃ t, t.Countable ∧ ⋃ x ∈ t, interior (U x) = Set.univ- Defined in
- Mathlib.Topology.Compactness.Lindelof
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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
- Filterstatement · cited by 8,121
- nhdsstatement and proof · cited by 5,554
- Set.univstatement and proof · cited by 3,945
- Set.iUnionstatement and proof · cited by 2,483
- interiorstatement and proof · cited by 714
- Set.Countablestatement and proof · cited by 545
- Set.mem_iUnionproof · cited by 212
- isOpen_interiorproof · cited by 130
- mem_interior_iff_mem_nhdsproof · cited by 82
- Set.univ_subset_iffproof · cited by 49
Cited by1
Results whose statement or proof uses this declaration.
- countable_cover_nhdsproof · cited by 0