Topological Manifold

Definition

$(M,\mathcal{T})$ A Locally Euclidean second-countable Hausdorff Space Topological Space $(M,\mathcal{T})$ is a topological manifold.

A one-dimensional manifold is called a curve, and a two-dimensional manifold is called a surface.

Facts

The Product Space of an $n$-dimensional manifold and an $m$-dimensional manifold is an $(n+m)$-dimensional manifold.

Consider an $n$-dimensional manifold without boundary $X$ and an $m$-dimensional manifold with boundary $Y$. Then, $\partial (X\times Y)=X\times \partial Y$