Theorems · Definition · general topology
PrimitiveSpectrum.kernel
{α : Type u_1} → [CompleteLattice α] → {T : Set α} → Set ↑T → αFor a subset S of T, kernel S is the infimum of S (considered as a set of α)
- Defined in
- Mathlib.Topology.Order.HullKernel
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 10 from the axioms · uses no axioms
- Assumes
- CompleteLattice
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 and proof · cited by 7,166
- Set.imageproof · cited by 5,609
- CompleteLatticestatement and proof · cited by 1,048
- InfSet.sInfproof · cited by 935
Cited by7
Results whose statement or proof uses this declaration.
- PrimitiveSpectrum.OrderGeneratesproof · cited by 3
- PrimitiveSpectrum.gcstatement · cited by 2
- PrimitiveSpectrum.hull_kernel_of_isClosedstatement 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.closedsGC_closureOperatorstatement and proof · cited by 0