A Wecken theorem for n-valued maps

In [6] Schirmer (1985) established that, if φ:X⊸X is an n-valued map defined on a compact triangulable manifold of dimension at least three, then the appropriate Nielsen number, N(φ), is a sharp lower bound for the number of fixed points in the n-valued homotopy class of φ. In this note we generalize this theorem by allowing X to be any compact polyhedron without local cut points and such that no connected component is a two-manifold.