Vol. 52, No. 1, 1974

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Fixed point sets of polyhedra

Helga Schirmer

Vol. 52 (1974), No. 1, 221–226

It is shown that every closed nonempty subset of a polyhedron can be the fixed point set of a suitable self-map if the polyhedron satisfies a certain connectedness condition. Hence the same is true for all compact triangulable manifolds with or without boundary. The proof uses existing results on deformations of polyhedra with a minimum number of fixed points if the dimension of the polyhedron is at least two, and on self-maps of dendrites with given fixed point sets if the dimension of the polyhedron is one.

Mathematical Subject Classification 2000
Primary: 54H25
Secondary: 57C05
Received: 14 December 1972
Published: 1 May 1974
Helga Schirmer