- Current Issue - Ahead of Print Articles - All Issues - Search - Open Access - Information for Authors - Downloads - Guideline - Regulations ㆍPaper Submission ㆍPaper Reviewing ㆍPublication and Distribution - Code of Ethics - For Authors ㆍOnlilne Submission ㆍMy Manuscript - For Reviewers - For Editors
 Imbeddings of manifolds defined on an $O$-minimal structure on $(\mathbb R,+,\cdot,<)$ Bull. Korean Math. Soc. 1999 Vol. 36, No. 1, 183-201 Tomohiro Kawakami Wakayama University Abstract : Let $M$ be an $o$-minimal structure on the standard structure $\frak R:=(\Bbb R, +,$ %\par\noindent $\cdot, <)$ of the field of real numbers. We study $C^r \frak S$ manifolds and $C^r \frak S$-$G$ manifolds $(0 \le r \le \omega)$ which are generalizations of Nash manifolds and Nash $G$ manifolds. We prove that if $M$ is polynomially bounded, then every $C^r \frak S$ $(0 \le r <\infty)$ manifold is $C^r \frak S$ imbeddable into some $\Bbb R^n$, and that if $M$ is exponential and $G$ is a compact affine $C^{\omega} \frak S$ group, then each compact $C^{\infty} \frak S$-$G$ manifold is $C^{\infty} \frak S$-$G$ imbeddable into some representation of $G$. Keywords : Nash $G$ manifolds, $C^{\infty} G$ manifolds, affine, $o$-minimal MSC numbers : 14P10, 14P15, 14P20, 57S05, 57S15, 58A07, 03C Downloads: Full-text PDF