The set of root classes plays a crucial role in the Nielsen root theory. Extending Brown et al.`s work on the set of root classes of iterates of maps, we rearrange it into the reduced orbit set and show that under suitable hypotheses, any reduced orbit has the full depth property as in the Nielsen type theory of periodic orbits.
roots of map iterates;reduced orbit sets;full depth property;
R. F. Brown, B. Jiang and H. Schirmer, Roots of iterates of maps, Topology Appl. 66 (1995), 129–157
B. Jiang, Lectures on Nielsen Fixed Point Theory, Contemporary Mathematics 14 American Mathematical Society, Providence, RI, 1983
B. Jiang, S. H. Lee, and M. H. Woo, Reidemeister orbit sets, Fund. Math. 183 (2004), 139–156
T. Kiang, The Theory of Fixed Point Classes, Springer, Berlin, 1989
E. Spanier, Algebraic Topology, McGraw-Hill, New York, 1966