categories: Re: banach operations

["P. Scott" <scpsg@matrix.cc.uottawa.ca>]

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