Abstract: By defining the parameters of the neuron neighborhood interactions, the self organizing learning algorithm is extended to the more general case. Then a theorem on the topology preserving neural network’s convergency is presented, by which a rigorous proof of the convergency of one dimensional neural networks with uniformly distributed input is presented. This paper revises and extends the existing results on the self organizing learning, and provides a new method for further proving the convergency of topology preserving neural networks completely.