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2. Lattice (order) - Wikipedia

   en.wikipedia.org/wiki/Lattice_(order)

   A lattice is an abstract structure studied in the mathematical subdisciplines of order theory and abstract algebra.It consists of a partially ordered set in which every pair of elements has a unique supremum (also called a least upper bound or join) and a unique infimum (also called a greatest lower bound or meet).

3. Lattice (group) - Wikipedia

   en.wikipedia.org/wiki/Lattice_(group)

   A lattice in the sense of a 3-dimensional array of regularly spaced points coinciding with e.g. the atom or molecule positions in a crystal, or more generally, the orbit of a group action under translational symmetry, is a translation of the translation lattice: a coset, which need not contain the origin, and therefore need not be a lattice in ...

4. Map of lattices - Wikipedia

   en.wikipedia.org/wiki/Map_of_lattices

   An algebraic lattice is complete. (def) 10. A complete lattice is bounded. 11. A heyting algebra is bounded. (def) 12. A bounded lattice is a lattice. (def) 13. A heyting algebra is residuated. 14. A residuated lattice is a lattice. (def) 15. A distributive lattice is modular. [3] 16. A modular complemented lattice is relatively complemented ...

5. Completeness (order theory) - Wikipedia

   en.wikipedia.org/wiki/Completeness_(order_theory)

   A poset is a complete lattice if and only if it is a cpo and a join-semilattice. Indeed, for any subset X, the set of all finite suprema (joins) of X is directed and the supremum of this set (which exists by directed completeness) is equal to the supremum of X. Thus every set has a supremum and by the above observation we have a complete lattice.

6. Algebraic structure - Wikipedia

   en.wikipedia.org/wiki/Algebraic_structure

   In mathematics, an algebraic structure or algebraic system [1] consists of a nonempty set A (called the underlying set, carrier set or domain), a collection of operations on A (typically binary operations such as addition and multiplication), and a finite set of identities (known as axioms) that these operations must satisfy.

7. Skew lattice - Wikipedia

   en.wikipedia.org/wiki/Skew_lattice

   The -class partition of a skew lattice , as indicated in the above diagrams, is the unique partition of into its maximal rectangular subalgebras, Moreover, is a congruence with the induced quotient algebra / being the maximal lattice image of , thus making every skew lattice a lattice of rectangular subalgebras.

8. Wisconsin school shooter was in contact with a California man ...

   www.aol.com/small-tight-knit-community-madison...

   Unanswered questions remain about a fatal shooting at a Madison, Wisconsin, private school as new details emerge about the shooter’s family life and possible ties to a California man who ...

9. Lattice (discrete subgroup) - Wikipedia

   en.wikipedia.org/wiki/Lattice_(discrete_subgroup)

   Let be a locally compact group and a discrete subgroup (this means that there exists a neighbourhood of the identity element of such that = {}).Then is called a lattice in if in addition there exists a Borel measure on the quotient space / which is finite (i.e. (/) < +) and -invariant (meaning that for any and any open subset / the equality () = is satisfied).