Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: About the uniqueness of the hyperspaces $C(p,X)$ in some classes of
  continua   Given a continuum $X$ and $p\in X$, we will consider the hyperspace $C(p,X)$
of all subcontinua of $X$ containing $p$. Given a family of continua
$\mathcal{C}$, a continuum $X\in\mathcal{C}$ and $p\in X$, we say that $(X,p)$
has unique hyperspace $C(p,X)$ relative to $\mathcal{C}$ if for each
$Y\in\mathcal{C}$ and $q\in Y$ 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 \cite{Corona.et.al(2019)}.

35
The categories of this paper are: mtrl-th
0
The categories of this paper are: hep-ph
21
The categories of this paper are: adap-org
34
The categories of this paper are: chem-ph
13
The categories of this paper are: quant-ph
33
The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio
22
The categories of this paper are: chao-dyn
32
The categories of this paper are: atom-ph
18
The categories of this paper are: econ
26
The categories of this paper are: bayes-an
17
The categories of this paper are: q-fin
36
The categories of this paper are: cmp-lg
20
The categories of this paper are: acc-phys
5
The categories of this paper are: gr-qc
19
The categories of this paper are: eess