Thermodynamics, Electricity, and Magnetism/Gauss' Law/Closed surface

A closed surface is a surface that is compact and without boundary. It may have finite edges (cube, prism etc.) or infinite edges (sphere, torus). Examples of closed surfaces include the sphere, the torus and the Klein bottle. Examples of non-closed surfaces include an open disk (which is a sphere with a puncture), a cylinder(which is a sphere with two punctures), and the Möbius strip.

A surface embedded in three-dimensional space is closed if and only if it is the boundary of a solid. As with any closed manifold, a surface embedded in Euclidean space that is closed with respect to the inherited Euclidean topology is not necessarily a closed surface.