This approximately 100 page thesis contains, in a very readable form, just about all one wants to know about the theory of domains, algebraic or continuous directed complete posets. Starting from the definition of a partial ordering, the author quickly gets to new results in domain theory. The work is divided into four chapters: Basic Concepts, Domains with least elements, Domains without a least element, and Continuous domains. The theme is to classify such domains by finding maximal subcategories with certain properties. The first such theorem is Smyth’s result that if D is an algebraic directed complete poset with least element and if the function space [D\(\to D]\) is \(\omega\)-algebraic, then D is bifinite. This theorem is generalized in the thesis in various ways: to the uncountable case, and to the case that the domains have no least element. The last chapter treats retracts of algebraic directed complete posets.
The paper is quite well-written and can serve as either an introduction to an interesting subject or as a source of conjectures and new results for the expert.