Theorems · Theorem · general topology
CompactSpace.elim_nhds_subcover
∀ {X : Type u} [inst : TopologicalSpace X] [CompactSpace X] (U : X → Set X),
(∀ (x : X), U x ∈ nhds x) → ∃ t, ⋃ x ∈ t, U x = ⊤- Defined in
- Mathlib.Topology.Compactness.Compact
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpaceCompactSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- Finsetstatement and proof · cited by 13,712
- Top.topstatement and proof · cited by 9,680
- Filterstatement · cited by 8,121
- nhdsstatement and proof · cited by 5,554
- Set.univproof · cited by 3,945
- Set.iUnionstatement and proof · cited by 2,483
- CompactSpacestatement and proof · cited by 593
- top_uniqueproof · cited by 102
- IsCompact.elim_nhds_subcoverproof · cited by 15
- CompactSpace.isCompact_univproof · cited by 14
Cited by5
Results whose statement or proof uses this declaration.
- Equicontinuous.comap_uniformFun_eqproof · cited by 3
- AlgebraicGeometry.exists_appTop_π_eq_of_isLimitproof · cited by 2
- AlgebraicGeometry.exists_appTop_map_eq_zero_of_isLimitproof · cited by 1
- AlgebraicGeometry.Scheme.exists_isQuasiAffine_of_isLimitproof · cited by 1
- ContinuousMap.sublattice_closure_eq_topproof · cited by 1