论文标题
可递归的可挤压套件是可挤压的
Recursively squeezable sets are squeezable
论文作者
论文摘要
在Freedman [F2]和Freedman-Quinn [FQ]的工作中，关于4个manifolds的拓扑，无效分解，其非辛氏元素在[MOR]的术语中是递归类似于恒星的过滤长度1的术语，并显示出可缩小的。 [MOR]的主要结果是涵盖这些类型的分解的一般定理。它建立了无效分解的收缩性，其非单明子元素是递归类似于星形的相等的集合，其过滤长度具有均匀的有限上限。结果是本文的灵感。这里表明，在过滤长度上有均匀有限上限的假设是不必要的。在轮廓中：定义了紧凑型公制空间的可挤压子集和可挤压子集的概念。可以观察到可挤压的类似星形的等效套件，并且任何可挤压的非单明元素元件的紧凑型公制空间的无效分解都是可缩小的。还可以证明，只有在可挤压的情况下，并且每个可递归的可扁平式套装都是可挤压的。因此，可递归挤压的紧凑型公制空间的任何无效分解都是可收缩的。后者定理的推论是[MOR]的主要结果，假设有限的上限在滤过长度上均匀。
In work by Freedman [F2] and Freedman-Quinn [FQ] on the topology of 4-manifolds, null decompositions whose non-singleton elements are, in the terminology of [MOR], recursively starlike-equivalent sets of filtration length 1 arise and are shown to be shrinkable. The main result of [MOR] is a general theorem covering these types of decompositions. It establishes the shrinkability of null decompositions whose non-singleton elements are recursively starlike-equivalent sets whose filtration lengths have a uniform finite upper bound. That result is the inspiration for this article. Here it is shown that the hypothesis of a uniform finite upper bound on filtration lengths is unnecessary. In outline: notions of squeezable subsets and squashable subsets of a compact metric space are defined. It is observed that starlike-equivalent sets are squeezable, and that any null decomposition of a compact metric space whose non-singleton elements are squeezable is shrinkable. It is also proved that a set is squeezable if and only if it is squashable, and that every recursively squashable set is squashable. It follows that any null decomposition of a compact metric space whose non-singleton elements are recursively squeezable is shrinkable. The latter theorem has as a corollary the main result of [MOR] with the hypothesis of a uniform finite upper bound on filtration lengths removed.
