their order structure or via their (Scott) topology. A lot is known

about their structural properties both at the individual and the

categorical level. In applications, in addition to the order structure

some algebraic operations satisfying certain equations are often

required. The interplay between order/topology and algebra is not

entirely straightforward but we do now have some general existence theorems.

In this talk I intend to present the various approaches to domain theory

that one might be interested in from an applications point of view, and

then explain the difficulties one has to overcome if one is trying to

add algebraic structure. In joint work with M. A. Moshier and S.

Vickers, we have found a new way of constructing domain algebras which

is much more concrete than the method that was employed before. More

recently still, K. Keimel and J. Lawson discovered that this can be

explained and extended very elegantly by replacing order with topology.

Robert Recorde Room

Department of Computer Science