SHORE POINTS IN DENDROIDS AND CONICAL POINTED HYPERSPACES

Abstract

If X is a continuum and mu a Whitney map for C(X), a subcontinuum Y of C(X) is mu-conical pointed if for some lambda is-an-element-of [0, 1), the cone K (mu--1(lambda) AND Y) of mu--1(lambda) AND Y is homeomorphic with mu--1[lambda, 1] AND Y. This property generalizes the Roger's cone = hyperspace property. If X is a (smooth) dendroid, x is-an-element-of X is a shore point if there is a sequence of subdendroids of X not containing x which converges to X. In this paper we give necessary and sufficient conditions on X, involving shore points, for C(p)(X) to be mu-conical pointed.