Fundamental class of real algebraic sets

Let F :Rn→Rk (n⩾k) be a polynomial mapping such that the real algebraic set X=F−1(0) is compact. There are introduced a fundamental class [X]F∈Hn−k(X;Z) and a topological degree deg(G) for G :X→Rn−k+1−{0}, which coincide with the usual ones when X is a smooth oriented m-manifold. There is also given an effective method for computing deg(G) and a formula for the degree on critical points of mappings Q :X→Rn−k.