In mathematics, topological degree theory is a generalization of the winding number of a curve in the complex plane.
It can be used to estimate the number of solutions of an equation, and is closely connected to fixed-point theory.
When one solution of an equation is easily found, degree theory can often be used to prove existence of a second, nontrivial, solution.
There is also a degree for continuous maps between manifolds.
Topological degree theory has applications in complementarity problems, differential equations, differential inclusions and dynamical systems.