2020/02/26 by Kazuhisa Shimakawa, Shimakawa, Kazuhisa
Arts and Humanities · Mathematics · #46T30 #54C35 #58D15 #Algebraic Topology (math.AT) #FOS: Mathematics #Mathematical and Theoretical Analysis #Philosophy and History of Science
paper · pdf · doi:10.48550/arxiv.2002.11339
openalex publication_date 2020/02/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.