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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2504.11136 |
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Table of Contents:
- We prove that the path space of a differentiable manifold is diffeomorphic to a Fréchet space, endowing the path space with a linear structure. Furthermore, the base point preserving mapping space consisting of maps from a cube to a differentiable manifold is also diffeomorphic to a Fréchet space. As a corollary of a more general theorem, we prove that the path fibration becomes a fibre bundle for manifolds M. Additionally, we discuss the mapping space from a compact topological space to a differentiable manifold, demonstrating that this space admits the structure of a smooth Banach manifold.