The Depths of Centers of Maps on a Class of Continua

摘要

According to the works of Xiong J.C. and Ye X.D. et al., the depth of the center of f is at most 2 when f is a continuous map on the unit interval; at most 3 when f is one on a tree; at most 4 when f is one on the Warsaw circle. Naturally, one expects to obtain an upper bound of the depth of the center of a map on other spaces. In this paper, we show that the depth of the of f is at most 2n provided that (I) f is a continuous map on a hereditarily decomposable chainable continuum X with order n, and (ii) the set of the nondegenerate elements in k-th layer of X is finite, where n∈N and k-1.2, n-1.