Polish空间是指一个可分、可完备度量化的拓扑空间。在本项目中，我们将研究Polish空间上的等价关系之间的Borel归约。我们尤其重视那些在Borel归约意义下复杂度处于较低位置的等价关系。本项目的主要目标是研究l_1等价关系，因为这个等价关系关联着描述集合论中的一个非常重要的公开问题。我们希望能够确定l_1等价关系在Borel归约图中的确切位置。我们也将关注l_p类型等价关系和可数等价关系。我们将试图刻画这些等价关系之间的Borel归约图的结构。对这两类等价关系的研究将有助于研究l_1等价关系。

A Polish space is a separable, completely metrizable topological space. In this project, we study Borel reduction between equivalence relations on Polish spaces. Particularly, we focus on the equivalence relations which are of lower complexity under Borel reduction. The main purpose of this project is to investigate the l_1 equivalence relation, for this equivalence relation connects to a very important open problem in descriptive set theory. We expect to determine the exact position of l_1 equivalence relation in the diagram of equivalence relations under Borel reduction. We also pay attention to l_p like equivalence relations and countable equivalences. We are going to learn the structure of the diagram of Borel reduction within these equivalence relations. The study on these two kinds of equivalence relations is helpful for the study on l_1 equivalence relation.