Domain representations of topological spaces

A domain representation of a topological space X is a function, usually a quotient map, from a subset of a domain onto X . Several di erent classes of domain representations are introduced and studied. It is investigated when it is possible to build domain representations from existing ones. It is, for example, discussed whether there exists a natural way to build a domain representation of a product of topological spaces from given domain representations of the factors. It is shown that any T0 topological space has a domain representation. These domain representations are very large. However, smaller domain representations are also constructed for large classes of spaces. For example, each second countable regular Hausdor space has a domain representation with a countable base. Domain representations of functions and function spaces are also studied. c © 2000 Elsevier Science B.V. All rights reserved.