Vol. 48, No. 1, 1973

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Weakly almost periodic homeomorphisms of the two sphere

W. K. Mason

Vol. 48 (1973), No. 1, 185–196

A self-homeomorphism f of the 2-sphere S2 is weakly almost periodic (w.a.p.) if the collection of orbit closures forms a continuous decomposition of S2. It is shown that if f is orientation-preserving, w.a. p. and nonperiodic, then f has exactly two fixed points, and every nondegenerate orbit closure is an homology l-sphere. There is an example with an orbit closure which is an homology l-sphere but not a real l-sphere. If f is orientation-reversing, w.a. p. and has a fixed point, then f is shown to be periodic. The orbit structure of orientation-reversing, w.a. p., nonperiodic homeomorphisms on S2 is studied.

Mathematical Subject Classification 2000
Primary: 54H20
Received: 12 June 1972
Revised: 24 August 1972
Published: 1 September 1973
W. K. Mason