About complexity and dimension of continuous finite-dimensional maps

he definition of the $\epsilon$-complexity of an individual continuous finite-dimensional map is proposed. This concept is in line with general idea of A.N.Kolmogorov on how to quantify the complexity of an object. It is established that for "almost any" Hölder map the $\epsilon$-complexity admits an effective description allowing us to use this concept for development of model-free technologies of classification and segmentation for multidimensional data of arbitrary nature. A new definition of the dimension for a graph of finite-dimensional continuous map following from the concept of the $\epsilon$-complexity is also proposed.