$n$值映射的划分

摘要：

$n$值映射是集值连续函数$f$，使得$f(x)$对于每个$x$都具有基数$n$。某些$n$值映射将“分裂”为$n$单值映射的并集。分裂的刻画一直是$n$ -值映射拓扑理论中的一个重要课题。在本文中，我们考虑更一般的概念“分区”的$n$值的地图，其中一个给定的地图被分解成一个联合的其他地图，可能不是单值的。我们推广了几个分裂特征，这将描述分区的混合配置空间和混合辫群，连通分支的$f$的图。我们证明了一些例子的想法。我们还讨论了$n$ -值映射的不动点理论及其划分，并与Crabb的有限值映射理论建立了联系。

英文摘要：

An $n$-valued map is a set-valued continuous function $f$ such that $f(x)$ has cardinality $n$ for every $x$. Some $n$-valued maps will "split" into a union of $n$ single-valued maps. Characterizations of splittings has been a major theme in the topological theory of $n$-valued maps. In this paper we consider the more general notion of "partitions" of an $n$-valued map, in which a given map is decomposed into a union of other maps which may not be single-valued. We generalize several splitting characterizations which will describe partitions in terms of mixed configuration spaces and mixed braid groups, and connected components of the graph of $f$. We demonstrate the ideas with some examples on tori. We also discuss the fixed point theory of $n$-valued maps and their partitions, and make some connections to the theory of finite-valued maps due to Crabb.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。