Which classes of functions can a given multilayer perceptron approximate?

Given a multilayer perceptron (MLP), there are functions that can be approximated up to any degree of accuracy by the MLP without having to increase the number of the hidden nodes. Those functions belong to the closure F̄ of the set F of the maps realizable by the MLP. In the paper, we give a list of maps with this property. In particular, it is proven that rationales belongs to F̄ for networks with arctangent activation function and exponentials belongs to F̄ for networks with sigmoid activation function. Moreover, for a restricted class of MLPs, we prove that the list is complete and give an analytic definition of F̄