Approximation to separated functions on Cartesian product spaces

Abstract

Introduction: The purpose of this paper is to generalize some results contained in _Some theorems of Chebyshev's approximations_, by D. J. Newman and H. S. Shapiro [3], and to exhibit the failure of certain other generalizations. This problem was suggested by Professor Donald J. Newman ; I wish to acknowledge, with deep gratitude, his innumerable helpful suggestions and constant encouragement. ¶ The work has been carried out, in part, under N. S. F. Summer Fellowships for Graduate Teaching Assistants (1964 and 1965). ¶ Numbers in brackets refer to the bibliography at the end of the paper.