Banič and Kennedy (2015) [8] have drawn attention to a natural but largely unexplored field of study in the theory of inverse limits with set-valued functions, namely using bonding functions having graphs that are arcs. At the end of that paper they pose a question: If $f:[0,1]\to 2^{[0,1]}$ is an upper semi-continuous function such that $G(f^n)$ is connected for each n and $G(f)$ is an arc, is $\underleftarrow{\lim }\mathit{f}$ connected? In this paper we provide a negative answer to that question, include some additional examples as well as a theorem on trivial shape (not requiring that the graphs be arcs), and pose several questions concerning, for the most part, inverse limits with set-valued functions whose graphs are arcs.

Banič 和 Kennedy (2015) [8] 已经引起了人们对具有设置值函数的逆极限理论中一个自然但很大程度上未开发的研究领域的关注，即使用具有弧形图的键合函数。在那篇论文的结尾，他们提出了一个问题：如果$F：[0,1]\to 2^{[0,1]}$ 是一个上半连续函数，使得 $G(F^n)$对于每个n和$G(F)$ 是圆弧，是 $\underleftarrow{\mathrm{林}}\mathit{F}$连接的？在本文中，我们对这个问题给出了否定的答案，包括一些额外的例子以及一个关于平凡形状的定理（不要求图是弧线），并提出了几个问题，在大多数情况下，与 set-图形为弧的值函数。