关于整体半解析集的不可约分支
On the irreducible components of globally defined semianalytic sets
摘要：
本文提出了实解析流形$M$的顺从半解析子集$C$的概念，并研究了这类集的主要性质.顺从的$C$ -半解析集可以理解为全局定义的半解析集，它具有关于Zebriki闭包的整洁行为。这一事实使我们能够发展一个自然的定义不可约和相应的理论不可约成分的顺从$C$ -半解析集。这些概念将平行的概念推广到复代数集和解析集、$C$ -解析集、Nash集和半代数集。
英文摘要：
In this work we present the concept of amenable $C$-semianalytic subset of a real analytic manifold $M$ and study the main properties of this type of sets. Amenable $C$-semianalytic sets can be understood as globally defined semianalytic sets with a neat behavior with respect to Zariski closure. This fact allows us to develop a natural definition of irreducibility and the corresponding theory of irreducible components for amenable $C$-semianalytic sets. These concepts generalize the parallel ones for: complex algebraic and analytic sets, $C$-analytic sets, Nash sets and semialgebraic sets.
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