Certain posets X have a binary operationMathworldPlanetmath join denoted by , such that xy is the least upper bound of x and y. Such posets are called join-semilattices, or -semilattices, or upper semilattices.

If j and j are both joins of x and y, then jj and jj, and so j=j; thus a join, if it exists, is unique. The join is also known as the or operator.

Title join
Canonical name Join
Date of creation 2013-03-22 12:27:40
Last modified on 2013-03-22 12:27:40
Owner yark (2760)
Last modified by yark (2760)
Numerical id 11
Author yark (2760)
Entry type Definition
Classification msc 06A12
Synonym or operator
Related topic Meet
Related topic Semilattice
Defines join-semilattice
Defines join semilattice
Defines upper semilattice