Topological manifold
A topological manifold is a second countable Hausdorff space that is locally homeomorphic to Euclidean space.
- $X$ is second countable Hausdorff space
- $ \forall x\in X,\; \exist N\in\mathcal{N}_x \;\text{s.t.}$ $N$ and $\R^n$ are homeomorphic
If then, $X$ is an $n$-dimensional topological manifold.
A klein bottle, which is the example of 2-dimensional topological manifold