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High Quality Content by WIKIPEDIA articles! In the mathematical fields of order and domain theory, a Scott domain is an algebraic, bounded complete cpo. It has been named in honour of Dana S. Scott, who was the first to study these structures at the advent of domain theory. Scott domains are very closely related to algebraic lattices, being different only in possibly lacking a greatest element.Since the empty set certainly has some upper bound, we can conclude the existence of a least element (the supremum of the empty set) from bounded completeness. Also note that, while the term "Scott domain" is widely used with this definition, the term "domain" does not have such a general meaning: it may be used to refer to many structures in domain theory and is usually explained before it is used.