Ernest Michael and Theory of Selections 3 24
نویسنده
چکیده
For a large number of those working in topology, functional analysis, multivalued analysis, approximation theory, convex geometry, mathematical economics, control theory, and several other areas, the year 1956 has always been strongly connected with the publication by Ernest Michael of two fundamental papers on continuous selections which appeared in the Annals of Mathematics [4] [5]. With sufficient precision that year marked the beginning of the theory of continuous selections of multivalued mappings. In the last fifty years the approach to multivalued mappings and their selections, set forth by Michael [4] [5], has well established itself in contemporary mathematics. Moreover, it has become an indispensable tool for many mathematicians working in vastly different areas. Clearly, the principal reason for this is the naturality of the concept of selection. In fact, many mathematical assertions can be reduced to using the linguistic reversal “∀x ∈ X ∃y ∈ Y . . . ”. However, as soon as we speak of the validity of assertions of the type
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