Computational Effects in Topological Domain Theory

This paper contributes towards establishing the category QCB, of topological quotients of countably based spaces, and its subcategory TP, of topological predomains, as a flexible framework for denotational semantics of programming languages. In particular, we show that both categories have free algebras for arbitrary countable parametrised equational theories, and are thus, following ideas of Plotkin and Power, able to model a wide range of computational effects. Furthermore, we give an explicit construction of the free algebras.