Coherent Continuous Systems and the Generalized Functional Equation of Associativity
King-Tim Mak
Source abstract
A theory of coherent continuous systems is outlined. Systems are to be decomposed hierarchically into modules. For this purpose, some results on the structure of continuous functions are adapted to generalize the classic 3-Modules Theorem of binary systems. Consideration of the modular structure of coherent continuous systems leads naturally to the generalized functional equation of associativity G(g(u, v), w) = H(u, h(v, w)) involving four unknown 2-place continuous functions. The functional equation is solved under some regularity conditions motivated by the properties of coherent continuous systems. The solutions obtained give rise to generalized notions of parallel and series system structures.
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