homomorphism of topological groups

例句：

1. 1. In mathematics, a homomorphism is a functionthat preserves the structure of a group.
   在数学中，同构映射是一种函数，它保持群的结构。
2. 2. The studyof homomorphisms has led to importantadvances in computer science.
   研究同构映射的研究在计算机科学中取得了重要的进展。
3. 3. The concept of homomorphism is crucialfor understanding the behavior of groups and theiroperations.
   同构映射的概念对于理解群的行为及其操作至关重要。