Theorems · Definition · general topology
PrimitiveSpectrum.OrderGenerates
{α : Type u_1} → [CompleteLattice α] → Set α → PropT order generates α if, for every a in α, there exists a subset of T such that a is
the kernel of S.
- Defined in
- Mathlib.Topology.Order.HullKernel
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 11 from the axioms · uses no axioms
- Assumes
- CompleteLattice
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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.Elemproof · cited by 7,166
- CompleteLatticestatement and proof · cited by 1,048
- PrimitiveSpectrum.kernelproof · cited by 5
Cited by4
Results whose statement or proof uses this declaration.
- PrimitiveSpectrum.hull_kernel_of_isClosedstatement and proof · cited by 1
- PrimitiveSpectrum.kernel_hullstatement and proof · cited by 1
- PrimitiveSpectrum.gistatement and proof · cited by 1
- PrimitiveSpectrum.closedsGC_closureOperatorstatement and proof · cited by 0