Ample fields as a basis for possibilistic processes

Ample fields play an important role in possibility theory. These fields of subsets of a universe, which are additionally closed under arbitrary unions , act as the natural domains for possibility measures. A set provided with an ample field is then called an ample space. In this paper we generalise W ang's notions of product ample field and product ample space. We make a top ological study of ample spaces and their products, and introduce ample subs paces, extensions and one-point extensions of ample spaces. In this way, a first step towards a mathematical theory of possibilistic processes is made . (C) 2001 Elsevier Science B.V. All rights reserved.