Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Author: Zappala, Emanuele
Institution: Idaho State University
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7212033939