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C1-triangulations of semialgebraic sets
| Title: | C1-triangulations of semialgebraic sets |
| Authors: | Ohmoto, Toru Browse this author | | Shiota, Masahiro Browse this author |
| Keywords: | semialgebraic sets | | subanalytic sets | | X-sets | | o-minimal category | | triangulation | | curve selection lemma | | differential forms | | piecewise algebraic differential forms | | de Rham homotopy theory |
| Issue Date: | Sep-2017 |
| Publisher: | John Wiley & Sons |
| Journal Title: | Journal of topology |
| Volume: | 10 |
| Issue: | 3 |
| Start Page: | 765 |
| End Page: | 775 |
| Publisher DOI: | 10.1112/topo.12024 |
| Abstract: | We show that every semialgebraic set admits a semialgebraic triangulation such that each closed simplex is C-1 differentiable. As an application, we give a straightforward definition of the integration integral(omega)(X) over a compact semialgebraic subset X of a differential form. 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. |
| Rights: | This is the peer reviewed version of the following article: Ohmoto, T. and Shiota, M. (2017), C1-triangulations of semialgebraic sets. Journal of Topology, 10: 765–775, which has been published in final form at doi:10.1112/topo.12024. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving. |
| Type: | article (author version) |
| URI: | http://hdl.handle.net/2115/71421 |
| Appears in Collections: | 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > 雑誌発表論文等 (Peer-reviewed Journal Articles, etc)
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Submitter: 大本 亨(おおもと とおる)
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