论文标题
差异空间之间的广义图
Generalized maps between diffeological spaces
论文作者
论文摘要
通过利用哥伦布的广义功能的概念，我们在任意差异空间之间引入了渐近图的概念。由差异空间和渐近图组成的类别在差异空间的类别上丰富，并遗传了完整性和结合性。特别是，欧几里得开放式集合上的一组渐近函数包括施瓦茨分布，并在鲁滨逊的渐近数领域形成了哥伦布类型的平滑差异代数。为了说明我们的机械的实用性，我们表明，如果我们利用渐近图而不是光滑的渐变图，则可以建立平滑相对细胞复合物的同型扩展特性。
By utilizing the idea of Colombeau's generalized function, we introduce a notion of asymptotic map between arbitrary diffeological spaces. The category consisting of diffeological spaces and asymptotic maps is enriched over the category of diffeological spaces, and inherits completeness and cocompleteness. In particular, the set of asymptotic functions on a Euclidean open set include Schwartz distributions and form a Colombeau type smooth differential algebra over Robinson's field of asymptotic numbers. To illustrate the usefulness of our machinery, we show that homotopy extension property can be established for smooth relative cell complexes if we exploit asymptotic maps instead of smooth ones.
