This construction plays a key role in the classification of closed surfaces.

Imagine a closed surface in the form of cylinder around line charge in its wall.

Thus, the Klein bottle is a closed surface with no distinction between inside and outside.

On a closed surface like this, the angles of a triangle always add up to more than 180 (Figure 2.3).

A real polyhedron has two faces at each edge such that the boundary forms a closed surface.

This equation only works if the integral is done over a closed surface.

It can be proved that any closed surface will have at least four points called umbilical points.

They would form a closed surface, like the surface of the earth.

Any massive object can be thought of as a closed surface with a certain amount of entropy.

The classification of closed surfaces gives an affirmative answer to the analogous question in two dimensions.