Neural Networks in Fr\'echet spaces

We derive approximation results for continuous functions from a Fréchet space X into its field F. The approximation is similar to the well known universal approximation theorems for continuous functions from Rn to R, where approximation is done with (multilayer) neural networks [10, 16, 12, 20]. Similar to classical neural networks, the approximating functions that we obtain are easy to implement and allows for fast computation and fitting.

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