A characterization of extendable connectivity functions
Let \(f: I\to I\) be a function where \(I=[0,1]\). In this paper a family of peripheral intervals for f is defined and the following theorems are proved. Theorem 1. If a family of peripheral intervals exists for \(f: I\to I\), then f is the restriction of a connectivity function g: I \(2\to I\) such that g is continuous on the complement of \(I\times 0\) where I is embedded in I 2 as \(I\times 0.\) Theorem 2. The existence of a family of peripheral intervals is both necessary and sufficient that a function \(f: I\to I\) be the restriction of a connectivity function g: I \(2\to I\) where I is embedded in I 2 as \(I\times 0\).
scientific article; zbMATH DE number 4040199
scientific article