We prove that the category of -manifolds has all finite products. Further, we show that a -manifold (resp., a -morphism) can be reconstructed from its algebra of global -functions (resp., from its algebra morphism between global -function algebras). These results are of importance in the study of Lie groups. The investigation is all the more challenging, since the completed tensor product of the structure sheafs of two -manifolds is not a sheaf. We rely on a number of results on (pre)sheaves of topological algebras, which we establish in the appendix.

中文翻译：

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-歧管类别中的产品

我们证明-流形的范畴具有所有有限积。此外，我们证明了一个 -manifold (resp., a -morphism) 可以从它的 global -functions 的代数（resp., from its algebramorphism between global -function algebras）重建。这些结果在李群的研究中具有重要意义。研究更具挑战性，因为两个流形的结构层的完整张量积不是层。我们依赖于我们在附录中建立的拓扑代数的（预）层上的许多结果。