Universal approximation of continuous maps between topological vector spaces

Emanuele Zappala

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arXiv · 2609.07942

Universal approximation of continuous maps between topological vector spaces

Emanuele Zappala

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Abstract

We study the problem of universal approximation of continuous maps between topological vector spaces by neural networks. We provide a universal approximation theorem for maps between locally convex topological vector spaces with and without paracompactness assumptions. We extend this result to continuous maps between non-locally convex topological vector spaces on compact and convex sets under the assumption of finite topological dimension.

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Emanuele Zappala. 2026-09-07. Universal approximation of continuous maps between topological vector spaces. https://arxiv.org/abs/2609.07942

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