On the analysis and synthesis of certain abstract systems
Reese T. Prosser · Bulletin of the American Mathematical Society · 1971
The systems considered here are those describable as continuous functions mapping one compact metric space into another.A class of such systems is determinable if the members can be distinguished to within a given error by a finite number of elementary measurements made on the domain and range spaces.Such classes are necessarily relatively compact in the uniform metric and admit a common modulus of continuity.This announcement provides quantitative estimates of the number of measurements required in terms of the common modulus of continuity of the class, and the metric entropy, capacity, and dimension of the domain and range spaces.These data are used to construct uniform simplicial and polynomial approximations for each member of the class, and to provide quantitative estimates for the degrees of the approximating polynomials required.