topological manifold

Definition

An $n$-dimensional topological manifold $M$ is a topological space such that

• $M$ is Hausdorff
• $M$ is second-countable
• $M$ is locally Euclidean of dimension $n$

Notes

• manifold may mean topological space that is locally Euclidean, but usually more formally defined to also require Hausdorff and second-countable condtions

References

1. http://staff.ustc.edu.cn/~wangzuoq/Courses/18F-Manifolds/Notes/Lec01.pdf
2. J. M. Lee, Introduction to smooth manifolds, Second edition. in Graduate texts in mathematics, no. 218. New York Heidelberg Dordrecht London: Springer, 2013, pp. 2-3.
3. https://mathworld.wolfram.com/Manifold.html
4. https://ncatlab.org/nlab/show/manifold
5. https://math.stackexchange.com/questions/1211762/what-is-a-manifold
6. https://www.bananaspace.org/wiki/流形