有限图的超空间$C(p,X)$
Hyperspaces $C(p,X)$ of finite graphs
摘要：
给定一个连续统$X$和$p\in X$，我们将考虑包含$p$的$X$的所有子连续统的超空间$C(p,X)$和所有超空间$C(q,X)$的族$K(X)$，其中$q\in X$ .本文给出了有限图$X$的点$p,q\in X$上的一些条件，以保证$C(p,X)$和$C(q,X)$同胚.同时，我们还研究了有限图$X$的均匀度与$K(X)$中拓扑不同空间的个数（称为$K(X)$的大小）之间的关系.此外，我们构造每个正整数$n$，一个有限的图形$X_n$，使$K(X_n)$的大小$n$，我们提出了一个定理，允许构造有限的图形$X$与家庭$K(X)$的大小不同程度的同质性。
英文摘要：
Given a continuum $X$ and $p\in X$, we will consider the hyperspace $C(p,X)$ of all subcontinua of $X$ containing $p$ and the family $K(X)$ of all hyperspaces $C(q,X)$, where $q\in X$. In this paper we give some conditions on the points $p,q\in X$ to guarantee that $C(p,X)$ and $C(q,X)$ are homeomorphic, for finite graphs $X$. Also, we study the relationship between the homogeneity degree of a finite graph $X$ and the number of topologically distinct spaces in $K(X)$, called the size of $K(X)$. In addition, we construct for each positive integer $n$, a finite graph $X_n$ such that $K(X_n)$ has size $n$, and we present a theorem that allows to construct finite graphs $X$ with a degree of homogeneity different from the size of the family $K(X)$.
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