关于实解析轨道折叠的次解析子集
On subanalytic subsets of real analytic orbifolds
摘要：
本文的目的是在实解析orbifolds的背景下定义半解析和次解析子集和映射，并研究它们的基本性质。我们证明结果类似于一些著名的结果在流形的情况下。例如，我们证明了：如果$A$是实解析商orbifold $X$的子解析子集，则存在与$A$维数相同的实解析orbifold $Y$和具有$f(Y)=A$的真解析映射$f\colon Y\to X$.我们还研究了次解析集的象和逆象，证明了如果$X$和$Y$是实解析轨道，并且如果$f\colon X\to Y$是次解析映射，则$Y$的任何次解析子集PDMATHAMT的逆象$f^{-1}(B)$是次解析的.此外，如果$f$是适当的，则$X$的任何子分析子集$A$的像$f(A)$也是适当的。
英文摘要：
The purpose of this paper is to define semi- and subanalytic subsets and maps in the context of real analytic orbifolds and to study their basic properties. We prove results analogous to some well-known results in the manifold case. For example, we prove that if $A$ is a subanalytic subset of a real analytic quotient orbifold $X$, then there is a real analytic orbifold $Y$ of the same dimension as $A$ and a proper real analytic map $f\colon Y\to X$ with $f(Y)=A$. We also study images and inverse images of subanalytic sets and show that if $X$ and $Y$ are real analytic orbifolds and if $f\colon X\to Y$ is a subanalytic map, then the inverse image $f^{-1}(B)$ of any subanalytic subset $B$ of $Y$ is subanalytic. If, in addition, $f$ is proper, then also the image $f(A)$ of any subanalytic subset $A$ of $X$ is proper.
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