On shallow feedforward neural networks with inputs from a topological space

arXiv:2504.02321v3 Announce Type: replace Abstract: We study feedforward neural networks with inputs from a topological space (TFNNs). We prove a universal approximation theorem for shallow TFNNs, which demonstrates their capacity to approximate any continuous function defined on this topological space. As an application, we obtain an approximative version of Kolmogorov's superposition theorem for compact metric spaces.