We consider the problem of feature extraction and determination of intrinsic dimensionality of observation data. One of the common approaches to this problem is to use autoassociative neural networks with a "bottleneck" projecting layer. We propose a different approach in which a neural network performs a topological mapping that creates a nonlinear lower-dimensional projection of the data. The mapping preserves relative distances of neighbors. This technique can be efficiently implemented with the help of radial basis function networks, and it is significantly faster than training an autoassotiative network. We show that the proposed technique can be used for estimating the dimension of minimal mathematical model from time series data.