强内集与广义光滑函数
Strongly internal sets and generalized smooth functions
摘要：
基于Colombeau理论中的内集概念的一个改进，即所谓的强内集，我们引入了广义光滑函数空间，它是Colombeau广义函数的极大扩展.广义光滑函数作为广义点集之间的态射形成拓扑空间范畴的一个子范畴。特别地，它们可以不受限制地组成。
英文摘要：
Based on a refinement of the notion of internal sets in Colombeau's theory, so-called strongly internal sets, we introduce the space of generalized smooth functions, a maximal extension of Colombeau generalized functions. Generalized smooth functions as morphisms between sets of generalized points form a sub-category of the category of topological spaces. In particular, they can be composed unrestrictedly.
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