The minimum theorem for the relative root Nielsen number

Commun. Korean Math. Soc. 1997 Vol. 12, No. 3, 701-707

Ki-Yeol Yang Sunchon National University

Abstract : In [8], we introduce the relative root Nielsen number $N(f;X,A,c)$ for maps of pairs of spaces $ f:(X,A) \to (Y,B)$. From it, we obtain some immediate consequences of the definition and illustrate it by some examples. We consider the question whether there exists a map $ g:(X,A) \to (Y,B)$ homotopic to a given map $ f:(X,A) \to (Y,B) $ which has precisely $N(f;X,A,c)$ roots, that is, the minimum theorem for $N(f;X,A,c)$.