Topological Manifold
- Differential Geometry 1.1

06 Feb 2023 in Mathematics on Differential Geometry · 1 min

from 「Geometrical Methods of Mathematical Physics」: Bernard F. Schutz

• Topological manifold

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