C1-triangulations of semialgebraic sets
| Autor: | Masahiro Shiota, Toru Ohmoto |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Triangulation (topology)
Semialgebraic set Pure mathematics Simplex Differential form 010102 general mathematics Mathematics::Optimization and Control 0102 computer and information sciences Computer Science::Computational Geometry 01 natural sciences Manifold Mathematics::Logic Real closed field Geometric measure theory 010201 computation theory & mathematics Computer Science::Symbolic Computation Geometry and Topology Differentiable function 0101 mathematics Mathematics |
| Zdroj: | Journal of Topology. 10:765-775 |
| ISSN: | 1753-8416 |
| Popis: | We show that every semialgebraic set admits a semialgebraic triangulation such that each closed simplex is C1 differentiable. As an application, we give a straightforward definition of the integration ∫Xω over a compact semialgebraic subset X of a differential form ω on an ambient semialgebraic manifold. This provides a significant simplification of the theory of semialgebraic singular chains and integrations without using geometric measure theory. Our results hold over every (possibly non-archimedian) real closed field. |
| Databáze: | OpenAIRE |
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