CONGRUENCE RELATIONS ON TOTALLY CONVEX-SPACES

Let X be a totally convex space and let ˜ be a congruence relation on X. In section I we give a simple and complete description of the congruence classes that are contained in the interior. Section 2 deals with those congruence classes, which are not contained in the interior, and some general results are derived. Section 3 gives a detailed description of the latter congruence classes in case X is separated. In section 4 we enumerate all congruence relations on the free totally convex space on two generators. The last section gives a complete characterization of all two-generated totally convex spaces and closes with a pictorial representation of each of them. © 1990, Taylor & Francis Group, LLC. All rights reserved.