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What (who) is upper semilattice - definition

PARTIALLY ORDERED SET IN WHICH EVERY NONEMPTY FINITE SET HAS A LEAST UPPER BOUND OR IN WHICH EVERY NONEMPTY FINITE SET HAS A GREATEST LOWER BOUND

Upper semi-lattice; Join-semilattice; Meet-semilattice; Meet semilattice; Join semilattice; Semi-lattice; Semilattices; Upper semilattice; Lower semilattice; Subsemilattice; Lower semi-lattice; Join semi-lattice; Meet semi-lattice; Upper-semilattice

Semilattice

In mathematics, a join-semilattice (or upper semilattice) is a partially ordered set that has a join (a least upper bound) for any nonempty finite subset. Dually, a meet-semilattice (or lower semilattice) is a partially ordered set which has a meet (or greatest lower bound) for any nonempty finite subset.

https://en.wikipedia.org/wiki/Semilattice

Upper school

IN ENGLAND, SCHOOLS WITHIN SECONDARY EDUCATION; SECTION OF A LARGER SCHOOL

Upper School; Upper schools

Upper schools in the UK are usually schools within secondary education. Outside England, the term normally refers to a section of a larger school.

https://en.wikipedia.org/wiki/Upper_school

upper school

IN ENGLAND, SCHOOLS WITHIN SECONDARY EDUCATION; SECTION OF A LARGER SCHOOL

Upper School; Upper schools

¦ noun

1. (in the UK) a secondary school for children aged from about fourteen upwards.

2. the section of a school comprising or catering for the older pupils.

Wikipedia

Semilattice

In mathematics, a join-semilattice (or upper semilattice) is a partially ordered set that has a join (a least upper bound) for any nonempty finite subset. Dually, a meet-semilattice (or lower semilattice) is a partially ordered set which has a meet (or greatest lower bound) for any nonempty finite subset. Every join-semilattice is a meet-semilattice in the inverse order and vice versa.

Semilattices can also be defined algebraically: join and meet are associative, commutative, idempotent binary operations, and any such operation induces a partial order (and the respective inverse order) such that the result of the operation for any two elements is the least upper bound (or greatest lower bound) of the elements with respect to this partial order.

A lattice is a partially ordered set that is both a meet- and join-semilattice with respect to the same partial order. Algebraically, a lattice is a set with two associative, commutative idempotent binary operations linked by corresponding absorption laws.

https://en.wikipedia.org/wiki/Semilattice