Abstract
A basic problem in fixed point theory is to find the least number of fixed points for a homotopy class of maps. That is, given a map f : X ~ X of a connected compact polyhedron X into itself, to find M F [ f ] :=Min{ #Fix (g) lg~f :X,X} . The invariant central to this theory is the Nielson number N(f) , defined as the number of essential fixed point classes (see [1] ~)r [4]). N( f ) is always a lower bound to MF[f] and it has been a long-standing problem to prove or to disprove that N ( f ) = MFEf ]. We know [3] that if X has no local cut points and X is not a surface of negative Euler characteristic, then N ( f ) = M F [ f ] for every map f : X , X . The aim of the present paper is to generalize the result of [5] and to show
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