拓扑流形的定义为：拓扑空间在满足以下条件时，称为维流形，即

1. 为豪斯多夫空间，
2. 对于任意一点，存在包含的维坐标邻域。

In topology, a branch of mathematics, a topological manifold is a topological space (which may also be a separated space) which locally resembles real n-dimensional space in a sense defined below. Topological manifolds form an important class of topological spaces with applications throughout mathematics.