Smooth surface
= Smooth surface
= Regular surface
{synonym}
A smooth surface in $\mathbb R^3$ is a two-dimensional smooth embedded submanifold. Locally it is parametrized by two coordinates with linearly independent tangent vectors.
A smooth surface is a two-dimensional <smooth manifold> whose underlying space is a <topological surface>. Its underlying topological space is a surface, but the smooth structure is extra data.