HervésBeloso, Carlos and Monteiro, Paulo Klinger (2009): Existence, continuity and utility representation of strictly monotonic preferences on continuum of goods commodity spaces.

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Abstract
It is an easy task for most commodity spaces, to find examples of strictly monotonic preference relations. For example, in the space of bounded sequences of real numbers.. However, it is not easy for spaces like the space of bounded functions defined in the real interval [0, 1]. In this note we investigate the roots of this difficulty. We show that strictly monotonic preferences on the space of bounded function on any set K always exist. However, if K is uncountable no such preference is continuous and none of them have a utility representation.
Item Type:  MPRA Paper 

Original Title:  Existence, continuity and utility representation of strictly monotonic preferences on continuum of goods commodity spaces 
Language:  English 
Keywords:  utility representation/ strictly monotonic preferences 
Subjects:  D  Microeconomics > D1  Household Behavior and Family Economics > D11  Consumer Economics: Theory B  History of Economic Thought, Methodology, and Heterodox Approaches > B5  Current Heterodox Approaches > B50  General 
Item ID:  15157 
Depositing User:  Carlos HervésBeloso 
Date Deposited:  11. May 2009 01:47 
Last Modified:  16. Feb 2013 02:22 
References:  Debreu, G., 1954, Representation of a preference ordering by a numerical function, in: R.M. Thrall, C.H. Coombs and R.L. Davis, eds., Decision Processes (Wiley, New York) 159165; also in Mathematical economics: twenty papers of Gerard Debreu (Cambridge University Press, Cambridge), 105110. Estévez, M. and Hervés, C., 1995, On the existence of continuous preference orderings without utility representations, Journal of Mathematical Economics 24, 305309. Kelley, J., General Topology, 1955, Graduate Texts in Mathematics 27 Monteiro, P. K., 1987, Some results on the existence of utility functions on path connected spaces, Journal of Mathematical Economics, 147156. 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/15157 