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Bibliographic Details
Main Author: Pinaud, Matthieu F.
Format: Preprint
Published: 2025
Subjects:
Online Access:https://arxiv.org/abs/2506.03366
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Table of Contents:
  • Let $M$ be a compact smooth manifold with corners and $N$ be a finite dimensional smooth manifold without boundary which admits local addition. We define a smooth manifold structure to general sets of continuous mapings $\mathcal{F}(M,N)$ whenever functions spaces $\mathcal{F}(U,\mathbb{R})$ on open subsets $U\subseteq [0,\infty)^n$ are given, subject to simple axioms. Construction and properties of spaces of sections and smoothness of natural mappings between spaces $\mathcal{F}(M,N)$ are discussed, like superposition operators $\mathcal{F}(M,f):\mathcal{F}(M,N_1)\to \mathcal{F}(M,N_2)$, $η\mapsto f\circ η$ for smooth maps $f:N_1\to N_2$.