Continuously differentiable functions on compact sets
Classical Analysis and ODEs
2020-06-18 v2
Abstract
We consider the space of real-valued continuously differentiable functions on a compact subset of a euclidean space. We characterize the completeness of this space and prove that the space of restrictions of continuously differentiable functions on the ambient space is always dense. The space is then compared with other spaces of differentiable functions on compact sets.
Cite
@article{arxiv.2003.09681,
title = {Continuously differentiable functions on compact sets},
author = {Leonhard Frerick and Laurent Loosveldt and Jochen Wengenroth},
journal= {arXiv preprint arXiv:2003.09681},
year = {2020}
}
Comments
15 pages