We characterize the simple rational functions of $n$ real variables which are discontinuous but continuous when restricted to any hyperplane. The characterization is expressed by simple inequalities with respect to the exponents of each variable. In particular, the following functions have such properties:

More generally, for every n>1 the functions constitute the examples we mentioned above. Finally, the smallest degree of the denominators of such examples is also investigated.

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**Last modified May 18, 2017.**