Theorems · Definition · general topology
PrimitiveSpectrum.hull
{α : Type u_1} → [SemilatticeInf α] → (T : Set α) → α → Set ↑TFor a of type α the set of element of T which dominate a is the hull of a in T.
- Defined in
- Mathlib.Topology.Order.HullKernel
- Cited by
- 13 results in Mathlib
- Foundations
- Depth 5 from the axioms · uses no axioms
- Assumes
- SemilatticeInf
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
- Set.Elemstatement · cited by 7,166
- Set.preimageproof · cited by 4,946
- Set.Iciproof · cited by 1,070
- SemilatticeInfstatement and proof · cited by 634
Cited by14
Results whose statement or proof uses this declaration.
- PrimitiveSpectrum.isClosed_iffstatement and proof · cited by 2
- PrimitiveSpectrum.gcstatement · cited by 2
- PrimitiveSpectrum.hull_finsetInfstatement and proof · cited by 2
- PrimitiveSpectrum.hull_infstatement · cited by 1
- PrimitiveSpectrum.hull_kernel_of_isClosedstatement and proof · cited by 1
- PrimitiveSpectrum.isOpen_iffstatement and proof · cited by 1
- PrimitiveSpectrum.isTopologicalBasis_relativeLowerstatement and proof · cited by 1
- PrimitiveSpectrum.kernel_hullstatement and proof · cited by 1
- PrimitiveSpectrum.gc_closureOperatorstatement and proof · cited by 1
- PrimitiveSpectrum.gistatement · cited by 1
- PrimitiveSpectrum.hull_iSupstatement · cited by 0
- PrimitiveSpectrum.hull_sSupstatement · cited by 0