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This is a Quantitative Study study.

October 5, 2025Open Access

Manifolds of mappings associated with real-valued function spaces and natural mappings between them

Key Points

Smooth manifold structures can be defined for sets of continuous mappings between various manifolds.
The superposition operators are crucial in analyzing the mappings between function spaces more broadly.
The construction discussed satisfies simple axioms, enhancing our understanding of function spaces and their smoothness.
Natural mappings between spaces of sections are explored, contributing to the theory of continuous mappings and manifolds.

Abstract

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 F (M, N) whenever functions spaces F (U, R) on open subsets U [0, ) ⁿ are given, subject to simple axioms. Construction and properties of spaces of sections and smoothness of natural mappings between spaces F (M, N) are discussed, like superposition operators F (M, f): F (M, N₁) F (M, N₂), η f η for smooth maps f: N₁ N₂.

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Cite This Study

Matthieu F. Pinaud (Tue,) studied this question.

synapsesocial.com/papers/68e25559d6d66a53c2474fba https://doi.org/https://doi.org/10.48550/arxiv.2506.03366

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