Computing with infinite objects

Abstract Infinite objects are often represented by words which may be of infinite length. For example the real numbers are given by possibly infinite decimal fractions. Starting from such a coding c:C → S we show how to actually compute with infinite objects belonging to the set S . We further introduce the topology TOP( c ) induced by c and prove that every computable function is continuous. For T 0 -topologies TOP( c ) we give a sufficient criteria for the coding c , which imply the computability of the minimal (with respect to TOP( c )) solution of any fixpoint equation. To compute the result of the composition of functions and to solve fixpoint equations, we use a special kind of network of parallel processes built up in a modular way.