Algebraicity versus analyticity (Q1060327)

This is a survey paper about the following two very connected topics: the equivalence between: (a) analytic and algebraic sets; and (b) analytic and algebraic functions (i.e. polynomials, Nash functions). It deals with both local and global theory. Especially the important contribution of the author and his collaborators is recorded. See: the author and \textit{W. Kucharz}, J. Reine Angew. Math. 352, 1-14 (1984; Zbl 0558.32002) and the author, \textit{W. Kucharz} and \textit{M. Shiota}, Invent. Math. 70, 115-156 (1982; Zbl 0502.32021)].