In topology, the winding number is an alternate term for the degree of a continuous mapping.

One may define a degree of a function between cycles, analogous to the degree of a continuous mapping.

Homology and cohomology: Betti numbers, Euler characteristic, degree of a continuous mapping.

The topological quantum number of a solution is sometimes called the winding number of the solution, or, more precisely, it is the degree of a continuous mapping.

In the context of this work, Brouwer also generalized the Jordan curve theorem to arbitrary dimension and established the properties connected with the degree of a continuous mapping.

In topology, the degree of a continuous mapping between two compact oriented manifolds of the same dimension is a number that represents the number of times that the domain manifold wraps around the range manifold under the mapping.