Domain Representable Spaces Defined by Strictly Positive Induction

Recursive domain equations have natural solutions. In particular there aredomains defined by strictly positive induction. The class of countably baseddomains gives a computability theory for possibly non-countably basedtopological spaces. A $ qcb_{0} $ space is a topological space characterized byits strong representability over domains. In this paper, we study strictlypositive inductive definitions for $ qcb_{0} $ spaces by means of domainrepresentations, i.e. we show that there exists a canonical fixed point ofevery strictly positive operation on $qcb_{0} $ spaces.Comment: 48 pages. Accepted for publication in Logical Methods in Computer Scienc