On the cardinality of indifference classes

Gerhard Herden, Andreas Pallack

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

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References

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Universitat Politècnica de València

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