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論文情報

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アクセス権	open access
URI	https://hdl.handle.net/2115/71421
タイトル	C1-triangulations of semialgebraic sets
著者	著者名 Ohmoto, Toru
	著者名 Shiota, Masahiro
言語	英語
キーワード	semialgebraic sets
	subanalytic sets
	X-sets
	o-minimal category
	triangulation
	curve selection lemma
	differential forms
	piecewise algebraic differential forms
	de Rham homotopy theory
発行日	2017-09
出版者	John Wiley & Sons
収録物名	Journal of topology
巻(号)	10(3)
ページ	765-775
抄録	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.
資源タイプ	学術雑誌論文
出版タイプ	Accepted Manuscript
権利情報	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.
PISSN	1753-8416
関連情報 (isVersionOf)	出版社版DOI https://doi.org/10.1112/topo.12024

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