Re: banach operations

Re Mike Barr's comments on Isbell's construction of unit balls, and Vaughan's remarks on Conway's construction, there is a paper by Denis Higgs (Proc. Koninklijke Nederlandse Akademie, Series A, Vol. 81, (4), 1978, pp.448-455) called: "A Universal Characterization of [0,\infty]", in which he gives such a characterization, based on a class of infinitary algebras in which the infinitary operation arises from the observation that every element of [0,\infty] can be wrtten as a sum, in general infinite, of fractions 1/{2^n} 's. Indeed, as Higgs' shows, this characterizes [0,\infty] as a free algebra of the appropriate kind on one generator. Cheers, Phil Scott