21. Similar conclusions hold for least elements . 22. Complete lattices and orders with a least element ( the " empty supremum " ) provide further examples. 23. Every recursively enumerable ( or even hyperarithmetic ) nonempty subset of this total ordering has a least element . 24. Equivalently, one may define an atom to be an element that is covers the least element "'0 " '. 25. As defined in set theory, the maximum and minimum of a greatest and least elements in the set, respectively. 26. Dcpos with a least element ( " pointed dcpos " ) are called complete partial order ( cpo ). 27. The College Logo combines the Logos of St . Brendan s and Shaw Colleges, or at least elements from each. 28. By definition, this is the least element among all elements that are greater than each member of the empty set. 29. By the above reasoning the map exists and is unique since least elements of subsets of wellordered sets are unique. 30. In the case of topologies, the greatest element is the discrete topology and the least element is the trivial topology.
