Concerning similarity transformations of linearly ordered sets

Abstract

Introduction. As is well known, two linearly ordered sets A and B are said to be similar if there exists a 1-1 correspondence between their elements which preserves order. A function which defines such a 1-1 correspondence may be called a similarity transformation on A to B. In this note we consider two problems concerning similarity transformations which do not seem to have received attention heretofore. The first problem is the following: