homotopy type of topological spaces

例句：

1. 1.In the study of topology, homotopy theory is a crucial concept.
   在拓扑学研究中，同胚理论是一个关键的概念。
2. 2.The geometry of the space is determined by the properties of its homotopy types.
   该空间的几何性质由其同胚类型的属性确定。
3. 3. The study of homotopy types in topological spaces has led to important advances in mathematical analysis.
   拓扑空间中同胚类型的研究在数学分析领域取得了重要的进展。