Definitions 1. 2-d [[Manifolds|manifold]]. A subset $S \subset \mathbb{R}^{3}$ is called a surface if, $\forall \underline{p} \in S,$ there exists an open set $U\subseteq \mathbb{R}^{2},$ and open set $V\subseteq \mathbb{R}^{3}$ containing such that $U$ is *homeomorphic* to $S \cap V.$ 2. [[Parametrized Surface]]. 3. [[Algebraic Surface]]. # Related - [[Curve]]