Eliakim Hastings Moore's ``General Analysis''
Like main stream functional analysis (or topological vector spaces) the two approaches (before and after 1915) of E. H. Moore (1862-1932) toward his General Analysis (GA) originated from linear integral equations. GA was to be a theory of classes of (numerically valued) functions, and of functional operations, involving at least one ``general'' variable on a ``general'' range. With the exception of the notion of Moore-Smith convergence (1922) Moore's work did not exert any temporary or lasting influence. Few of his many students at Chicago kept to his ideas, and did so only temporarily. The author presents a thorough research, based also on archival sources, of Moore's work in GA, as compared to that of Fréchet and others. He offers explanations, some of them of a sociological nature, for the failure of GA. Obvious reasons are the peculiar symbolic presentation (following Peano's), the lack of the concepts of vector spaces and of linearity, and the lack of applications (GA failed to consider eigenvalue problems). Though not so general as Moore pretended, GA was too general to produce significant results. The paper deserves attention as a case study on alternative approaches toward a significant field of modern mathematics. It shows that the historical development was not as straightforward and inevitable as other papers try to make believe.
scientific article; zbMATH DE number 1123668