2019/12/07 by Corona-Vázquez, Florencio, Quiñones-Estrella, Russell Aarón, Sánchez-Martínez, Javier
#FOS: Mathematics #General Topology (math.GN)
paper · doi:10.48550/arxiv.1912.03411
Given a continuum X and p∈ X, we will consider the hyperspace C(p,X) of all subcontinua of X containing p. Given a family of continua C, a continuum X\inC and p∈ X, we say that (X,p) has unique hyperspace C(p,X) relative to C if for each Y\inC and q∈ Y such that C(p,X) and C(q,Y) are homeomorphic, then there is an homeomorphism between X and Y sending p to q. In this paper we show that (X,p) has unique hyperspace C(p,X) relative to the classes of dendrites if and only if X is a tree, we present also some classes of continua without unique hyperspace C(p,X); this answer some questions posed in \citeCorona.et.al(2019).