From the point of view of musical performance, gestures are the movements of the body of the performer when playing an instrument. This vague idea can be modeled mathematically, by mixing category theory and topology, giving rise to the definition of a topological gesture with a given skeleton and body in a topological space. The skeleton represents the abstract configuration of the body's limbs and the topological space is a generalization of the three-dimensional space where the body's movements are usually modeled. The collection of all gestures with the same skeleton and body in a fixed space has a canonical topology, yielding a space of gestures. This article intends to show that the space of gestures $\mathrm{\Gamma }@X$ is homeomorphic to the function space $\mathbf{T}\mathbf{o}\mathbf{p}(|\mathrm{\Gamma }|,X)$, endowed with the compact-open topology. The topology of this space is the most natural choice for a space of functions, in the sense that it is related to the universal property of exponentials in the category of topological spaces. In particular, when the skeleton has a suitable property of finiteness, we show that the function space becomes a true exponential.

从音乐演奏的角度来看，手势是演奏乐器时演奏者身体的动作。通过将类别理论和拓扑结构混合在一起，可以用数学方法对这个模糊的想法进行建模，从而在拓扑空间中定义具有给定骨骼和身体的拓扑手势。骨骼代表人体四肢的抽象配置，拓扑空间是三维空间的概括，通常在三维空间中对人体的运动进行建模。在固定的空间中具有相同骨骼和身体的所有手势的集合具有规范的拓扑结构，从而产生了一个手势空间。本文旨在说明手势的空间$\mathrm{\Gamma }@X$ 与功能空间同胚 $\mathbf{Ť}\mathbf{Ø}\mathbf{p}（|\mathrm{\Gamma }|，X）$，具有紧凑开放式拓扑。从某种意义上说，此空间的拓扑与拓扑空间类别中的指数的通用属性有关，因此它是功能空间的最自然选择。特别是，当骨架具有合适的有限性时，我们证明函数空间变成了真实的指数。