ABSTRACT
General Remark. Part II (chapters 7-9) contains the topics of the functions of two variables, which are quite representative for the most topics of the multivariable functions. The counterexamples presented in this part of the work are separated into two groups. The rst one includes those examples that have intimate connections with counterexamples of one-variable functions considered in Part I. They show how the ideas applied in the one-dimensional case can be generalized/extended to many variables. Accordingly, the examples of this group are placed in the sections titled \one-dimensional links" in each of chapters 7-9. The examples of the second group have a weak or no connection with one-dimensional case, highlighting a specicity of concepts and results for multivariable functions. Some of them illustrate the situations that are feasible for two-variable functions but cannot happen in the case of one-variable functions. In each chapter, all the examples of the second group are collected in sections titled \multidimensional essentials".
