论文标题
连接的广义逆极限和中间值属性
Connected Generalized Inverse Limits and Intermediate Value Property
论文作者
论文摘要
在本文中，我们使用上半连续的设置值函数来考虑$ [0,1] $的逆极限。我们介绍了中间值属性的两个概括，并证明具有上半连续的设置值键合函数的逆极限，如果键合函数汇总，具有连接的图形，并且具有中间值属性的概括。举例说明，如果删除了任何条件，则结果一般不会得出。举例说明即使键合函数都没有中间值属性，也可能连接一个逆限制。此外，我们将设置值函数的结构与中间值属性的两种类型进行比较。
In this paper, we consider inverse limits of $[0,1]$ using upper semicontinuous set-valued functions. We introduce two generalizations of the Intermediate Value Property and prove that inverse limits with upper semicontinuous set-valued bonding functions are connected if the bonding functions are surjective, have connected graphs, and have either generalization of the Intermediate Value Property. Examples are given to demonstrate that if any of the conditions is dropped, the result does not hold in general. An example is given to show that an inverse limit may be connected even if the bonding functions do not have either Intermediate Value Property. Further, we compare the structures of set-valued functions with the two types of the Intermediate Value Property.
