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.

中文翻译：

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紧集上的连续可微函数

我们考虑欧几里德空间的紧凑子集上实值连续可微函数的空间。我们刻画了这个空间的完备性，并证明了环境空间上连续可微函数的限制空间总是稠密的。然后将该空间与紧集上的其他可微函数空间进行比较。