Arrow and Debreu always included the convexity of indifference curves amongst their 'assumptions'. The term 'assumptions' is a vague one which might refer to a presupposition underlying definitions as well as theorems, or to a premise which is needed only for the latter. Given that their definition does not include all equilibria which may exist when curves may be non-convex, it is possible that they meant the assumption of convexity in the former sense. Whether or not this is so, the definition has been widely adopted without any restriction of domain.