Vol. 36, No. 3, 1971

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Properties of fixed point sets on dendrites

Helga Schirmer

Vol. 36 (1971), No. 3, 795–810

Every nonempty closed subset of a dendrite can be the fixed point set of a self-map, but in general it cannot be the fixed point set of a map with special properties. Necessary conditions found here for the fixed point sets of homeomorphisms and monotone surjections of dendrites are mainly concerned with the order of the possible fixed points, and extend earlier results by G. E. Schweigert and L. E. Ward, Jr.

Mathematical Subject Classification
Primary: 54.85
Received: 9 July 1970
Published: 1 March 1971
Helga Schirmer