A COMPUTATIONAL MODEL FOR METRIC-SPACES

For every metric space X, we define a continuous poset BX such that X is homeomorphic to the set of maximal elements of BX with the relative Scott topology. The poset BX is a dcpo iff X is complete, and omega-c ontinuous iff X is separable. The computational model BX is used to gi ve domain-theoretic proofs of Banach's fixed point theorem and of two classical results of Hutchinson: on a complete metric space, every hyp erbolic iterated function system has a unique non-empty compact attrac tor, and every iterated function system with probabilities has a uniqu e invariant measure with bounded support. We also show that the probab ilistic power domain of BX provides an omega-continuous computational model for measure theory on a separable complete metric space X.