Topology does not discuss the concept of congruence between two graphs, but the concept of topological equivalence. For example, circles, squares and triangles are all equivalent graphs under topological transformation, although their shapes and sizes are different. Select some points on a sphere and connect them with disjoint lines, so that the sphere is divided into many blocks by these lines. Under topological transformation, the number of points, lines and blocks is still the same as the original number, which is topological equivalence.

It should be pointed out that torus does not have this property. Imagine that if the torus is cut, it will not be divided into many pieces, but will only become a curved barrel. In this case, we say that a sphere cannot be a torus topologically. Therefore, sphere and torus are topologically different surfaces.

The combination relationship and order relationship between points and lines on a straight line remain unchanged under topological transformation, which is a topological property. In topology, the closeness of curves and surfaces is also a topological property.