On the cardinality of indifference classes

Abstract

Let “≤” be a continuous total preorder on some topological space (X, t). Then the cardinality or at least lower and upper bounds of the cardinality of the indifference (equivalence) classes of “≤ ” will be computed. In addition, the relevance of these bounds in mathematical utility theory and the theory of orderable topological spaces will be discussed.

Keywords

• Indifference potency
• Calculable set
• Degree of connectedness
• Path rank
• Separation rank