(Swansea (on leave from Oslo))

The topological spaces which admit ?-admissible domain representations havebeen characterised as the qcb_0 spaces (i.e. T_0 quotients of countably

based spaces), and this forms a cartesian closed category with

(sequentially) continuous functions as morphisms. An algebraic domain is

defined by positive induction if it is the canonical solution of a

recursive domain equation which does not directly involve functions defined

on the space itself.

In this talk, we ask whether qcb_0 spaces admit definitions by positive

induction, and explain why it is a both natural and adequate choice to

consider domains with dense and local partial equivalence relations in

order to find a solution. We show that strictly positive operators on qcb_0

spaces have canonical fixed points, using the intuition of a fundamental

example. We briefly discuss why it seems reasonable to restrict ourselves

to Hausdorff spaces when searching for fixed points of general positive

operators.

Robert Record Room

Department of Computer Science