Bounded complete models of topological spaces

In this article we show that each complete metric space is the maximal point space of a continuous, bounded complete dcpo (in other common terminology, we show that such a space has a bounded complete computational model). This gives a positive answer to J. Lawsonʹs question of whether each completely metrizable space is the maximal point space of a continuous, bounded complete dcpo. (For related conjectures we refer the reader to the work of K. Martin cited below.) oposed solution to this well-known problem exhibits some fundamental links that hold between bitopological spaces, asymmetric topological structures and bounded complete computational models. In fact, the existence of a computational model for a topological space turns out to be equivalent to a number of fairly familiar concepts from asymmetric topology.