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Darboux property for functions of several variables

1963
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Transactions of the American Mathematical Society
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Introduction. Let En be the n-dimensional Euclidean space. A function /: E1 -ȣ! is said to have the Darboux property if for a < b and u between/(a), f(b) there is te(a,b) satisfying f(t) = u. There are several important classes of functions which possess the Darboux property : approximately continuous functions and ordinary or approximate derivatives. The purpose of this paper is to extend these results to En by introducing a Darboux notion for E" with the view of obtaining the following

doi:10.1090/s0002-9947-1963-0148811-6
fatcat:y6vqvxiv45bydon5piyiht2dcm