PreprintCC BY 4.0arXiv
Universal approximation of continuous maps between topological vector spaces
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 sets under the assumption of finite topological dimension.
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BibTeX
@misc{zappala2026universal,
title = {{Universal approximation of continuous maps between topological vector spaces}},
author = {Emanuele Zappala},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.07942},
eprint = {2609.07942},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.07942},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Universal approximation of continuous maps between topological vector spaces
AU - Emanuele Zappala
PY - 2026
DA - 2026/09/15
PB - arXiv
DO - 10.48550/arxiv.2609.07942
UR - https://arxiv.org/abs/2609.07942
AB - 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 sets under the assumption of finite topological dimension.
ER -