homeomorphism

Definition

Consider topological spaces $X$ and $Y$ to be homeomorphic if there exists a continuous map $f: X \to Y$ that is bijective (i.e. one-to-one and surjective) such that $f^{-1}$ is also continuous, where the mapping $f$ is called a homeomorphism.

References

1. http://staff.ustc.edu.cn/~wangzuoq/Courses/18F-Manifolds/Notes/Lec01.pdf