The Nielsen root number N(f ; c) of a map f : M → N at a point c ∈ N is a homotopy invariant lower bound for the number of roots at c, that is, for the cardinality of f−1(c). There is a formula for… Expand

Let f: (X, A)→(X, A) be an admissible selfmap of a pair of metrizable ANR's. A Nielsen number of the complement N(f; X, A) and a Nielsen number of the boundary n(f; X, A) are defined. N(f; X, A) is a… Expand

Abstract Let ⨍:X→X be a self-map of a compact ANR and A ⊂ X a closed subset. Two conditions are stated which are necessary for the realization of A as the fixed point set of a map g in the homotopy… Expand

Abstract Let ƒ:(X,A1,A2) → (X,A1,A2) be a selfmap of a triad which consist of a compact connected polyhedron X and two subpolyhedra A1 and A2 so that X = A1 ∪ A2. A Nielsen type number N(ƒ;A1 ∪ A2),… Expand

Abstract A relative root Nielsen number N rel (ƒ; c) is introduced which is a homotopy invariant lower bound for the number of roots at c for a map of pairs of spaces ƒ : (X, A) → (Y, B) and c ϵ Y .… Expand

Abstract Brouwer's homological degree has the multiplicative property for the composition of maps. That is, if f :X→Y and g :Y→Z are maps between closed oriented manifolds X,Y,Z of the same… Expand