Theorems · Inductive type · general topology
TopologicalLattice
(L : Type u_1) → [TopologicalSpace L] → [Lattice L] → Prop
Let L be a lattice equipped with a topology such that L has continuous infimum and supremum.
Then L is said to be a topological lattice.
- Defined in
- Mathlib.Topology.Order.Lattice
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 1 from the axioms · uses no axioms
- Assumes
- TopologicalSpaceLattice
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement · cited by 24,529
- Latticestatement · cited by 916
Cited by7
Results whose statement or proof uses this declaration.
- MeasureTheory.AEEqFun.coeFn_absstatement and proof · cited by 1
- ContinuousMap.mabs_applystatement and proof · cited by 0
- ContinuousMap.coe_absstatement and proof · cited by 0
- ContinuousMap.abs_applystatement and proof · cited by 0
- TopologicalLattice.casesOnstatement and proof · cited by 0
- TopologicalLattice.recOnstatement and proof · cited by 0
- ContinuousMap.coe_mabsstatement and proof · cited by 0