On the cardinality of indifference classes

Gerhard Herden; Andreas Pallack

doi:10.4995/agt.2004.1967

Authors

Gerhard Herden Universität Duisburg-Essen
Andreas Pallack Universität Duisburg-Essen

DOI:

https://doi.org/10.4995/agt.2004.1967

Keywords:

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

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.

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