This Research Note addresses several pivotal problems in spectral theo ry and nonlinear functional analysis in connection with the analysis o f the structure set of zeroes of a general class of nonlinear operator s. Appealing to a broad audience, it contains many important contribut ions to linear algebra, linear functional analysis, nonlinear function analysis, and topology. The author gives several applications of the abstract theory to reaction diffusion equations and system. The result s presented cover a thirty-year period and cut across a variety of mat hematical fields.