A Unified Constructive Approach to the Topological Degree in R n

The paper gives an approach to the topological degree in R n which takes into account numerical requirements and permits derivation of the known degree computation formulas in a simple way. The new approach subsumes several earlier approaches and represents a general principle of construction of degree computation formulas. The basic idea consists of computing the degree of a continuous function relative to a bounded open subset Ω of R n by means of an auxiliary function which is defined on a polyhedron approximating Ω and maps into a known fixed convex polyhedron containing the origin of R n . It is further shown that the topological degree of a continuous function relative to an n ‐dimensional polyhedron P can be computed alone by means of a subset of the boundary of P .