Definitions by positive induction in a category of domain representable spaces

Petter Kristian Kober

(Swansea (on leave from Oslo))

The topological spaces which admit ?-admissible domain representations have
been 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.

Thursday 18th October 2007, 14:00
Robert Record Room
Department of Computer Science