紧致化实解析函数及所得的里布空间
Compactifying real analytic functions and resulting Reeb spaces
AI总结：
自然地对连续映射进行紧致化，主要考虑实解析函数，通过里布空间研究其拓扑与组合性质，此前已获相关成果，现给出新讨论与例子。
摘要：
我们自然地制定连续映射的紧致化。主要考虑实解析函数。我们对所得显式映射的拓扑性质和组合性质感兴趣。为理解它们，我们使用它们的里布空间，它是函数定义域空间的商空间，由其水平集的相同分量中的两点识别的等价关系定义。在我们的情况或更一般的某些驯服情况下，它们已知是0维或1维（可度量的）胞腔复形。自上世纪以来，里布空间在大致理解函数和空间的拓扑性质和组合性质方面一直很重要。作者此前和最近都对这些紧致化进行了明确研究。我们已经得到了实代数函数，其里布空间不那么复杂，而且似乎是最自然和最简单的。我们给出了新的讨论和例子。
英文摘要：
We formulate compactifications of continuous maps naturally. We consider real analytic functions mainly. We are interested in topological properties and combinatorial ones of explicit resulting maps. For understanding them, we use their Reeb spaces, being quotient spaces of the spaces of the domains of the functions and defined by the equivalence relation identifying two points in same components of their level sets. They are known to be $0$- or $1$-dimensional (metrizable) cell-complexes, in our situations or more general certain tame cases. Reeb spaces have been important in understanding topological properties and combinatorial ones of functions and spaces roughly, since the last century. These compactifications have been explicitly studied by the author previously and recently. We have obtained real algebraic functions whose Reeb spaces are not so complicated and which seem to be of most natural and simplest. We present new discussions and examples.
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