Topology is the mathematical study of shapes and spaces. It is a major area of mathematics concerned with the most basic properties of space, such as connectedness, continuity and boundary. It is the study of properties that are preserved under continuous deformations including stretching and bending, but not tearing or gluing. 拓扑学（英语：topology）研究的是几何形体在连续形变，精确地说，双方一一而且双方连续的变换（称为同胚）之下保持不变的性质。理解得广泛些，拓扑学是研究数学中连续性现象的学科。
| 排名 |
学校 |
学校英文名 |
州/城市 |
| 1 |
加州大学伯克利分校 |
University of California–Berkeley |
Berkeley, CA |
| 2 |
哈佛大学 |
Harvard University |
Cambridge, MA |
| 3 |
普林斯顿大学 |
Princeton University |
Princeton, NJ |
| 4 |
麻省理工学院 |
Massachusetts Institute of Technology |
Cambridge, MA |
| 5 |
斯坦福大学 |
Stanford University |
Stanford, CA |
| 6 |
芝加哥大学 |
University of Chicago |
Chicago, IL |
| 7 |
哥伦比亚大学 |
Columbia University |
New York, NY |
| 8 |
德克萨斯大学奥斯汀分校 |
University of Texas–Austin |
Austin, TX |
| 9 |
密歇根大学安娜堡分校 |
University of Michigan–Ann Arbor |
Ann Arbor, MI |
| 10 |
康奈尔大学 |
Cornell University |
Ithaca, NY |
| 11 |
耶鲁大学 |
Yale University |
New Haven, CT |
| 12 |
纽约州立大学石溪分校 |
Stony Brook University–SUNY |
Stony Brook, NY |
| 13 |
加州大学戴维斯分校 |
University of California–Davis |
Davis, CA |
| 13 |
加州大学洛杉矶分校 |
University of California–Los Angeles |
Los Angeles, CA |
| 15 |
布朗大学 |
Brown University |
Providence, RI |
| 15 |
加州理工学院 |
California Institute of Technology |
Pasadena, CA |
参考资料：US NEWS Topology Rankings 2013/14 USNEWS排名